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Some interesting genus 2 curves
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Genus 2 curves over $\Q$
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Genus 2 curve labels
Label
Description
169.a.169.1
Modular curve $X_1(13)$
196.a.21952.1
Modular curve $X_0(28)$
249.a.249.1
First paramodular Jacobian
256.a.512.1
Modular curve $X_1(16)$
277.a.277.1
First proven example of the paramodular conjecture
324.a.648.1
Modular curve $X_1(18)$
336.a.172032.1
First non-square analytic order of Sha
363.a.11979.1
Isogenous to modular curve $X_0(33)/\langle w_3 \rangle$
450.a.2700.1
Isogenous to modular curve $X_0(30)/ \langle w_2 \rangle$
450.a.36450.1
Modular curve $X_0(30)/\langle w_{10} \rangle$
529.a.529.1
Isogenous to modular curve $X_0(23)$
587.a.587.1
Conjecturally first genus 2 curve of positive rank
676.a.562432.1
Modular curve $X_0(26)$
841.a.841.1
Isogenous to modular curve $X_0(29)$
961.a.923521.1
Modular curve $X_0(31)$
976.a.999424.1
Jacobian with 29-torsion point (largest known prime order)
1116.a.214272.1
39-torsion point
1225.a.6125.1
Isogenous to modular curve $X_0(35)/\langle w_7 \rangle$
1369.a.50653.1
Modular curve $X_0(37)$
2500.a.50000.1
Modular curve $X_0(50)$
2916.b.11664.1
Smallest known example of a genus 2 curve with $\mathrm{ST}^0(\mathrm{Jac}(X))=\mathrm U(1)$ (and with $\Aut(X_{\overline \Q})=C_3:D_4$).
3319.a.3319.1
Smallest known example of a genus 2 curve with analytic rank 2
4489.a.4489.1
Modular curve $X_0(67)/\langle w_{67} \rangle = X_0^+(67)$
5329.b.5329.1
Modular curve $X_0(73)/ \langle w_{73} \rangle = X_0^+(73)$
5547.b.16641.1
Modular curve $X_0(129)/ \langle w_{3}, w_{43} \rangle = X_0^*(129)$
8281.a.8281.1
Modular curve $X_0(91) / \langle w_{91} \rangle = X_0^+(91)$
10609.a.10609.1
Modular curve $X_0(103)/ \langle w_{103} \rangle = X_0^+(103)$
11449.a.11449.1
Modular curve $X_0(107)/\langle w_{107} \rangle = X_0^+(107)$
15625.a.15625.1
Modular curve $X_0(125) / \langle w_{125}\rangle = X_0^+(125)$
20736.l.373248.1
First QM curve
25913.a.25913.1
Smallest known example of a genus 2 curve with analytic rank 3
27889.a.27889.1
Modular curve $X_0(167)/ \langle w_{167} \rangle = X_0^+(167)$
35344.a.565504.1
Additional information
36481.a.36481.1
Modular curve $X_0(191)/ \langle w_{191} \rangle = X_0^+(191)$
440509.a.440509.1
Smallest known example of a genus 2 curve with analytic rank 4