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Table of non-hyperelliptic new modular curves of genus 3 and level N with Jacobian $ A_f$ of dimension 3



Table: Modular curves (without $ \mathbb{Q}$-rational Weierstrass point) with $ \mathbb{Q}$-simple Jacobian, $ N\leq 4000$
$ C_{109}^B$ $ x^3z - 2x^2yz - x^2z^2 - xy^3 + 6xy^2z - 6xyz^2 + 3xz^3 + y^4 - 6y^3z $
  $ +10y^2z^2 - 5yz^3=0$
$ C_{151}^A$ $ x^3z - 2x^2yz - 2x^2z^2 - xy^3 + 2xy^2z + 4xyz^2 + xz^3 + y^2z^2 - 3yz^3 - 2z^4=0 $
$ C_{179}^B$ $ x^3z - 2x^2yz - 2x^2z^2 - xy^3 + 2xy^2z + xyz^2 + 2xz^3 + y^2z^2 - yz^3 - z^4=0 $
$ C_{295}^{A}$ $ x^3z - x^2y^2 - x^2z^2 + xy^3 - xy^2z + 2xyz^2 - xz^3 - y^3z + 3y^2z^2 - yz^3=0 $
$ C_{369}^{F}$ $ x^3z - 2x^2z^2 - xy^3 + 6xyz^2 - 6xz^3 - 3y^2z^2 +6yz^3 - z^4=0 $
$ C_{855}^{L}$ $ x^3z - x^2z^2 - xy^3 + 3xyz^2 - 3xz^3 + 2y^3z - 3y^2z^2 + 3yz^3=0 $
$ C_{1215}^{P}$ $ x^3z - xy^3 + 3xyz^2 + 5xz^3 - 6y^2z^2 - 3yz^3 + z^4=0 $


Table: Modular curves (with $ \mathbb{Q}$-rational Weierstrass point) and with $ \mathbb{Q}$-simple Jacobian, $ N\leq 4000$
$ C_{97}^A$ $ x^3z - x^2y^2 - 5x^2z^2 + xy^3 + xy^2z + 3xyz^2 + 6xz^3 - 3y^2z^2 - yz^3 - 2z^4=0 $
$ C_{113}^C$ $ x^3z - x^2y^2 - 4x^2z^2 + xy^3 + 2xy^2z + 6xz^3 - y^3z - 3y^2z^2 + yz^3 - 3z^4=0$
$ C_{127}^A$ $ x^3z - x^2y^2 - 3x^2z^2 + xy^3 - xyz^2 + 4xz^3 + 2y^3z - 3y^2z^2 + 3yz^3 - 2z^4=0$
$ C_{139}^B$ $ x^3z - x^2y^2 - 2x^2z^2 + xy^3 - 2xy^2z + 2xyz^2 + xz^3 + y^4 - 2y^3z $
  $ + 4y^2z^2 - 3yz^3=0 $
$ C_{149}^A$ $ x^3z - x^2y^2 - 3x^2z^2 + xy^3 + 3xy^2z - 2xyz^2 + 2xz^3 - y^4 - y^2z^2 + yz^3=0 $
$ C_{169}^C$ $ x^3z - x^2y^2 - 3x^2z^2 + xy^3 + 2xyz^2 + xz^3 + y^2z^2 - 3yz^3 + z^4=0 $
$ C_{187}^E$ $ x^3z - x^2y^2 - x^2z^2 + xy^3 - xy^2z - xyz^2 + 2xz^3 + y^3z - y^2z^2 + 3yz^3=0 $
$ C_{203}^{F}$ $ x^3z - x^2y^2 - 3x^2z^2 + xy^3 + 3xy^2z - 4xyz^2 + 4xz^3 - y^4 + 3y^3z - 6y^2z^2 $
  $ + 3yz^3 - 2z^4=0 $
$ C_{217}^{A}$ $ 3x^3z - 3x^2y^2 - 11x^2z^2 - 3xy^3 + 13xy^2z - 2xyz^2 + 11xz^3- 2y^4 - y^3z $
  $ - 4y^2z^2 + yz^3 - 2z^4=0 $
$ C_{239}^{A}$ $ x^3z - x^2y^2 - x^2z^2 + xy^3 - xy^2z + xz^3 + y^4 - y^3z + yz^3 - z^4 =0$
$ C_{243}^{E}$ $ x^3z - 3x^2z^2 - xy^3 + 9xyz^2 - 6xz^3 + 2y^3z - 9y^2z^2 + 9yz^3 - 2z^4=0 $
$ C_{329}^{D}$ $ x^3z - x^2y^2 + xy^3 + xyz^2 + xz^3 - y^3z + 2yz^3 + z^4=0 $
$ C_{475}^{H}$ $ x^3z - x^2y^2 - 5x^2z^2 - xy^3 + xy^2z + 17xyz^2 + 14xz^3 - 2y^4 - 14y^3z $
  $ - 35y^2z^2 - 35yz^3 - 12z^4=0 $

$ C_{1175}^{D}$

 $ x^3z - x^2y^2 + x^2z^2 + xy^3 - 2xy^2z + 2xyz^2 - xz^3 + y^4 - 2y^3z + y^2z^2 + yz^3=0 $


See also the following table, where we also consider new modular non-hyperelliptic curves of genus 3 with splitted Jacobians. This table appears in :

  • E. Gonzalez-Jimenez, R. Oyono: Non-hyperelliptic modular curves of genus 3, Journal of Number Theory, 130 (2010), pp. 862-878.


    • Last update November 17, 2011