| Label |
Cremona label |
Class |
Cremona class |
Class size |
Class degree |
Conductor |
Discriminant |
Rank |
Torsion |
$\textrm{End}^0(E_{\overline\Q})$ |
CM |
Sato-Tate |
Semistable |
Potentially good |
Nonmax $\ell$ |
$\ell$-adic images |
mod-$\ell$ images |
Adelic level |
Adelic index |
Adelic genus |
Regulator |
$Ш_{\textrm{an}}$ |
Ш primes |
Integral points |
Modular degree |
Faltings height |
j-invariant |
$abc$ quality |
Szpiro ratio |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
| 6664.a1 |
6664a1 |
6664.a |
6664a |
$1$ |
$1$ |
\( 2^{3} \cdot 7^{2} \cdot 17 \) |
\( - 2^{10} \cdot 7^{8} \cdot 17^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$68$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$32256$ |
$1.270084$ |
$-1660932/4913$ |
$0.86662$ |
$4.38775$ |
$[0, 0, 0, -4459, 283318]$ |
\(y^2=x^3-4459x+283318\) |
68.2.0.a.1 |
$[]$ |
| 6664.f1 |
6664f1 |
6664.f |
6664f |
$1$ |
$1$ |
\( 2^{3} \cdot 7^{2} \cdot 17 \) |
\( - 2^{10} \cdot 7^{2} \cdot 17^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$68$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$4608$ |
$0.297129$ |
$-1660932/4913$ |
$0.86662$ |
$3.06166$ |
$[0, 0, 0, -91, -826]$ |
\(y^2=x^3-91x-826\) |
68.2.0.a.1 |
$[]$ |
| 13328.b1 |
13328f1 |
13328.b |
13328f |
$1$ |
$1$ |
\( 2^{4} \cdot 7^{2} \cdot 17 \) |
\( - 2^{10} \cdot 7^{2} \cdot 17^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$68$ |
$2$ |
$0$ |
$0.234418565$ |
$1$ |
|
$8$ |
$9216$ |
$0.297129$ |
$-1660932/4913$ |
$0.86662$ |
$2.83822$ |
$[0, 0, 0, -91, 826]$ |
\(y^2=x^3-91x+826\) |
68.2.0.a.1 |
$[(11, 34)]$ |
| 13328.y1 |
13328a1 |
13328.y |
13328a |
$1$ |
$1$ |
\( 2^{4} \cdot 7^{2} \cdot 17 \) |
\( - 2^{10} \cdot 7^{8} \cdot 17^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$68$ |
$2$ |
$0$ |
$5.205411486$ |
$1$ |
|
$0$ |
$64512$ |
$1.270084$ |
$-1660932/4913$ |
$0.86662$ |
$4.06752$ |
$[0, 0, 0, -4459, -283318]$ |
\(y^2=x^3-4459x-283318\) |
68.2.0.a.1 |
$[(4459/3, 294686/3)]$ |
| 53312.c1 |
53312bm1 |
53312.c |
53312bm |
$1$ |
$1$ |
\( 2^{6} \cdot 7^{2} \cdot 17 \) |
\( - 2^{16} \cdot 7^{8} \cdot 17^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$68$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$516096$ |
$1.616657$ |
$-1660932/4913$ |
$0.86662$ |
$3.93155$ |
$[0, 0, 0, -17836, -2266544]$ |
\(y^2=x^3-17836x-2266544\) |
68.2.0.a.1 |
$[]$ |
| 53312.d1 |
53312bf1 |
53312.d |
53312bf |
$1$ |
$1$ |
\( 2^{6} \cdot 7^{2} \cdot 17 \) |
\( - 2^{16} \cdot 7^{2} \cdot 17^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$68$ |
$2$ |
$0$ |
$0.467271532$ |
$1$ |
|
$6$ |
$73728$ |
$0.643703$ |
$-1660932/4913$ |
$0.86662$ |
$2.85883$ |
$[0, 0, 0, -364, -6608]$ |
\(y^2=x^3-364x-6608\) |
68.2.0.a.1 |
$[(46, 272)]$ |
| 53312.cj1 |
53312g1 |
53312.cj |
53312g |
$1$ |
$1$ |
\( 2^{6} \cdot 7^{2} \cdot 17 \) |
\( - 2^{16} \cdot 7^{8} \cdot 17^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$68$ |
$2$ |
$0$ |
$5.781243072$ |
$1$ |
|
$0$ |
$516096$ |
$1.616657$ |
$-1660932/4913$ |
$0.86662$ |
$3.93155$ |
$[0, 0, 0, -17836, 2266544]$ |
\(y^2=x^3-17836x+2266544\) |
68.2.0.a.1 |
$[(46/3, 39824/3)]$ |
| 53312.cm1 |
53312cl1 |
53312.cm |
53312cl |
$1$ |
$1$ |
\( 2^{6} \cdot 7^{2} \cdot 17 \) |
\( - 2^{16} \cdot 7^{2} \cdot 17^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$68$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$73728$ |
$0.643703$ |
$-1660932/4913$ |
$0.86662$ |
$2.85883$ |
$[0, 0, 0, -364, 6608]$ |
\(y^2=x^3-364x+6608\) |
68.2.0.a.1 |
$[]$ |
| 59976.h1 |
59976i1 |
59976.h |
59976i |
$1$ |
$1$ |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 17 \) |
\( - 2^{10} \cdot 3^{6} \cdot 7^{8} \cdot 17^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$68$ |
$2$ |
$0$ |
$3.397962489$ |
$1$ |
|
$2$ |
$451584$ |
$1.819389$ |
$-1660932/4913$ |
$0.86662$ |
$4.11059$ |
$[0, 0, 0, -40131, -7649586]$ |
\(y^2=x^3-40131x-7649586\) |
68.2.0.a.1 |
$[(415, 6868)]$ |
| 59976.bg1 |
59976m1 |
59976.bg |
59976m |
$1$ |
$1$ |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 17 \) |
\( - 2^{10} \cdot 3^{6} \cdot 7^{2} \cdot 17^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$68$ |
$2$ |
$0$ |
$4.067780593$ |
$1$ |
|
$2$ |
$64512$ |
$0.846435$ |
$-1660932/4913$ |
$0.86662$ |
$3.04935$ |
$[0, 0, 0, -819, 22302]$ |
\(y^2=x^3-819x+22302\) |
68.2.0.a.1 |
$[(151, 1828)]$ |
| 113288.b1 |
113288bc1 |
113288.b |
113288bc |
$1$ |
$1$ |
\( 2^{3} \cdot 7^{2} \cdot 17^{2} \) |
\( - 2^{10} \cdot 7^{2} \cdot 17^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$68$ |
$2$ |
$0$ |
$3.092703293$ |
$1$ |
|
$0$ |
$1327104$ |
$1.713736$ |
$-1660932/4913$ |
$0.86662$ |
$3.77701$ |
$[0, 0, 0, -26299, -4058138]$ |
\(y^2=x^3-26299x-4058138\) |
68.2.0.a.1 |
$[(2074/3, 39304/3)]$ |
| 113288.bc1 |
113288s1 |
113288.bc |
113288s |
$1$ |
$1$ |
\( 2^{3} \cdot 7^{2} \cdot 17^{2} \) |
\( - 2^{10} \cdot 7^{8} \cdot 17^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$68$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$9289728$ |
$2.686691$ |
$-1660932/4913$ |
$0.86662$ |
$4.78025$ |
$[0, 0, 0, -1288651, 1391941334]$ |
\(y^2=x^3-1288651x+1391941334\) |
68.2.0.a.1 |
$[]$ |
| 119952.by1 |
119952q1 |
119952.by |
119952q |
$1$ |
$1$ |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 17 \) |
\( - 2^{10} \cdot 3^{6} \cdot 7^{8} \cdot 17^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$68$ |
$2$ |
$0$ |
$0.820099068$ |
$1$ |
|
$4$ |
$903168$ |
$1.819389$ |
$-1660932/4913$ |
$0.86662$ |
$3.86696$ |
$[0, 0, 0, -40131, 7649586]$ |
\(y^2=x^3-40131x+7649586\) |
68.2.0.a.1 |
$[(-245, 1666)]$ |
| 119952.fx1 |
119952y1 |
119952.fx |
119952y |
$1$ |
$1$ |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 17 \) |
\( - 2^{10} \cdot 3^{6} \cdot 7^{2} \cdot 17^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$68$ |
$2$ |
$0$ |
$12.21210500$ |
$1$ |
|
$0$ |
$129024$ |
$0.846435$ |
$-1660932/4913$ |
$0.86662$ |
$2.86861$ |
$[0, 0, 0, -819, -22302]$ |
\(y^2=x^3-819x-22302\) |
68.2.0.a.1 |
$[(298579/71, 132465754/71)]$ |
| 166600.d1 |
166600u1 |
166600.d |
166600u |
$1$ |
$1$ |
\( 2^{3} \cdot 5^{2} \cdot 7^{2} \cdot 17 \) |
\( - 2^{10} \cdot 5^{6} \cdot 7^{2} \cdot 17^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$68$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$589824$ |
$1.101849$ |
$-1660932/4913$ |
$0.86662$ |
$3.04515$ |
$[0, 0, 0, -2275, -103250]$ |
\(y^2=x^3-2275x-103250\) |
68.2.0.a.1 |
$[]$ |
| 166600.bs1 |
166600bt1 |
166600.bs |
166600bt |
$1$ |
$1$ |
\( 2^{3} \cdot 5^{2} \cdot 7^{2} \cdot 17 \) |
\( - 2^{10} \cdot 5^{6} \cdot 7^{8} \cdot 17^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$68$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$4128768$ |
$2.074802$ |
$-1660932/4913$ |
$0.86662$ |
$4.01622$ |
$[0, 0, 0, -111475, 35414750]$ |
\(y^2=x^3-111475x+35414750\) |
68.2.0.a.1 |
$[]$ |
| 226576.c1 |
226576cl1 |
226576.c |
226576cl |
$1$ |
$1$ |
\( 2^{4} \cdot 7^{2} \cdot 17^{2} \) |
\( - 2^{10} \cdot 7^{8} \cdot 17^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$68$ |
$2$ |
$0$ |
$7.241449619$ |
$1$ |
|
$2$ |
$18579456$ |
$2.686691$ |
$-1660932/4913$ |
$0.86662$ |
$4.51154$ |
$[0, 0, 0, -1288651, -1391941334]$ |
\(y^2=x^3-1288651x-1391941334\) |
68.2.0.a.1 |
$[(1971, 61034)]$ |
| 226576.dn1 |
226576do1 |
226576.dn |
226576do |
$1$ |
$1$ |
\( 2^{4} \cdot 7^{2} \cdot 17^{2} \) |
\( - 2^{10} \cdot 7^{2} \cdot 17^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$68$ |
$2$ |
$0$ |
$1$ |
$4$ |
$2$ |
$0$ |
$2654208$ |
$1.713736$ |
$-1660932/4913$ |
$0.86662$ |
$3.56469$ |
$[0, 0, 0, -26299, 4058138]$ |
\(y^2=x^3-26299x+4058138\) |
68.2.0.a.1 |
$[]$ |
| 333200.b1 |
333200b1 |
333200.b |
333200b |
$1$ |
$1$ |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \cdot 17 \) |
\( - 2^{10} \cdot 5^{6} \cdot 7^{8} \cdot 17^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$68$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$8257536$ |
$2.074802$ |
$-1660932/4913$ |
$0.86662$ |
$3.79731$ |
$[0, 0, 0, -111475, -35414750]$ |
\(y^2=x^3-111475x-35414750\) |
68.2.0.a.1 |
$[]$ |
| 333200.gq1 |
333200gq1 |
333200.gq |
333200gq |
$1$ |
$1$ |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \cdot 17 \) |
\( - 2^{10} \cdot 5^{6} \cdot 7^{2} \cdot 17^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$68$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1179648$ |
$1.101849$ |
$-1660932/4913$ |
$0.86662$ |
$2.87917$ |
$[0, 0, 0, -2275, 103250]$ |
\(y^2=x^3-2275x+103250\) |
68.2.0.a.1 |
$[]$ |
| 479808.dc1 |
479808dc1 |
479808.dc |
479808dc |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17 \) |
\( - 2^{16} \cdot 3^{6} \cdot 7^{2} \cdot 17^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$68$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1032192$ |
$1.193008$ |
$-1660932/4913$ |
$0.86662$ |
$2.88254$ |
$[0, 0, 0, -3276, -178416]$ |
\(y^2=x^3-3276x-178416\) |
68.2.0.a.1 |
$[]$ |
| 479808.ey1 |
479808ey1 |
479808.ey |
479808ey |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17 \) |
\( - 2^{16} \cdot 3^{6} \cdot 7^{2} \cdot 17^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$68$ |
$2$ |
$0$ |
$2.845941525$ |
$1$ |
|
$2$ |
$1032192$ |
$1.193008$ |
$-1660932/4913$ |
$0.86662$ |
$2.88254$ |
$[0, 0, 0, -3276, 178416]$ |
\(y^2=x^3-3276x+178416\) |
68.2.0.a.1 |
$[(-26, 496)]$ |
| 479808.nh1 |
479808nh1 |
479808.nh |
479808nh |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17 \) |
\( - 2^{16} \cdot 3^{6} \cdot 7^{8} \cdot 17^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$68$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$7225344$ |
$2.165962$ |
$-1660932/4913$ |
$0.86662$ |
$3.77508$ |
$[0, 0, 0, -160524, 61196688]$ |
\(y^2=x^3-160524x+61196688\) |
68.2.0.a.1 |
$[]$ |
| 479808.pb1 |
479808pb1 |
479808.pb |
479808pb |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17 \) |
\( - 2^{16} \cdot 3^{6} \cdot 7^{8} \cdot 17^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$68$ |
$2$ |
$0$ |
$10.27249246$ |
$1$ |
|
$0$ |
$7225344$ |
$2.165962$ |
$-1660932/4913$ |
$0.86662$ |
$3.77508$ |
$[0, 0, 0, -160524, -61196688]$ |
\(y^2=x^3-160524x-61196688\) |
68.2.0.a.1 |
$[(1074886/5, 1114357616/5)]$ |
