| 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 |
| 1225.a1 |
1225j2 |
1225.a |
1225j |
$2$ |
$5$ |
\( 5^{2} \cdot 7^{2} \) |
\( - 5^{3} \cdot 7^{11} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.12.0.1 |
5B.4.1 |
$70$ |
$48$ |
$1$ |
$0.776960684$ |
$1$ |
|
$4$ |
$1920$ |
$1.027147$ |
$-2887553024/16807$ |
$0.98803$ |
$5.38589$ |
$[0, 1, 1, -7268, -242126]$ |
\(y^2+y=x^3+x^2-7268x-242126\) |
5.12.0.a.1, 10.24.0-5.a.1.2, 35.24.0-5.a.1.2, 70.48.1-70.d.1.3 |
$[(338, 6002)]$ |
| 1225.a2 |
1225j1 |
1225.a |
1225j |
$2$ |
$5$ |
\( 5^{2} \cdot 7^{2} \) |
\( - 5^{3} \cdot 7^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.12.0.2 |
5B.4.2 |
$70$ |
$48$ |
$1$ |
$0.155392136$ |
$1$ |
|
$6$ |
$384$ |
$0.222429$ |
$4096/7$ |
$0.98030$ |
$3.58488$ |
$[0, 1, 1, 82, 424]$ |
\(y^2+y=x^3+x^2+82x+424\) |
5.12.0.a.2, 10.24.0-5.a.2.1, 35.24.0-5.a.2.2, 70.48.1-70.d.2.2 |
$[(23, 122)]$ |
| 1225.b1 |
1225h2 |
1225.b |
1225h |
$2$ |
$37$ |
\( 5^{2} \cdot 7^{2} \) |
\( - 5^{3} \cdot 7^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$37$ |
37.114.4.2 |
37B.8.2 |
$5180$ |
$2736$ |
$97$ |
$6.477204378$ |
$1$ |
|
$2$ |
$1776$ |
$1.270485$ |
$-162677523113838677$ |
$1.07344$ |
$6.79971$ |
$[1, 1, 1, -208083, -36621194]$ |
\(y^2+xy+y=x^3+x^2-208083x-36621194\) |
20.2.0.a.1, 37.114.4.b.2, 148.228.10.?, 185.228.10.?, 259.342.16.?, $\ldots$ |
$[(1190, 36857)]$ |
| 1225.b2 |
1225h1 |
1225.b |
1225h |
$2$ |
$37$ |
\( 5^{2} \cdot 7^{2} \) |
\( - 5^{3} \cdot 7^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$37$ |
37.114.4.1 |
37B.8.1 |
$5180$ |
$2736$ |
$97$ |
$0.175059577$ |
$1$ |
|
$6$ |
$48$ |
$-0.534974$ |
$-9317$ |
$0.80290$ |
$2.53560$ |
$[1, 1, 1, -8, 6]$ |
\(y^2+xy+y=x^3+x^2-8x+6\) |
20.2.0.a.1, 37.114.4.b.1, 148.228.10.?, 185.228.10.?, 259.342.16.?, $\ldots$ |
$[(0, 2)]$ |
| 1225.c1 |
1225b4 |
1225.c |
1225b |
$4$ |
$14$ |
\( 5^{2} \cdot 7^{2} \) |
\( 5^{6} \cdot 7^{9} \) |
$0$ |
$\Z/2\Z$ |
$\Q(\sqrt{-7})$ |
$-28$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$2016$ |
$1.325109$ |
$16581375$ |
$1.19804$ |
$6.15884$ |
$[1, -1, 1, -45555, 3753572]$ |
\(y^2+xy+y=x^3-x^2-45555x+3753572\) |
|
$[]$ |
| 1225.c2 |
1225b3 |
1225.c |
1225b |
$4$ |
$14$ |
\( 5^{2} \cdot 7^{2} \) |
\( - 5^{6} \cdot 7^{9} \) |
$0$ |
$\Z/2\Z$ |
$\Q(\sqrt{-7})$ |
$-7$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$1$ |
$1008$ |
$0.978536$ |
$-3375$ |
$0.98030$ |
$5.02165$ |
$[1, -1, 1, -2680, 66322]$ |
\(y^2+xy+y=x^3-x^2-2680x+66322\) |
|
$[]$ |
| 1225.c3 |
1225b2 |
1225.c |
1225b |
$4$ |
$14$ |
\( 5^{2} \cdot 7^{2} \) |
\( 5^{6} \cdot 7^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q(\sqrt{-7})$ |
$-28$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$288$ |
$0.352154$ |
$16581375$ |
$1.19804$ |
$4.51688$ |
$[1, -1, 1, -930, -10678]$ |
\(y^2+xy+y=x^3-x^2-930x-10678\) |
|
$[]$ |
| 1225.c4 |
1225b1 |
1225.c |
1225b |
$4$ |
$14$ |
\( 5^{2} \cdot 7^{2} \) |
\( - 5^{6} \cdot 7^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q(\sqrt{-7})$ |
$-7$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$1$ |
$144$ |
$0.005581$ |
$-3375$ |
$0.98030$ |
$3.37969$ |
$[1, -1, 1, -55, -178]$ |
\(y^2+xy+y=x^3-x^2-55x-178\) |
|
$[]$ |
| 1225.d1 |
1225f2 |
1225.d |
1225f |
$2$ |
$37$ |
\( 5^{2} \cdot 7^{2} \) |
\( - 5^{3} \cdot 7^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$37$ |
37.114.4.2 |
37B.8.2 |
$5180$ |
$2736$ |
$97$ |
$1$ |
$1$ |
|
$0$ |
$12432$ |
$2.243439$ |
$-162677523113838677$ |
$1.07344$ |
$8.44167$ |
$[1, 0, 0, -10196068, 12530481277]$ |
\(y^2+xy=x^3-10196068x+12530481277\) |
20.2.0.a.1, 37.114.4.b.2, 148.228.10.?, 185.456.10.?, 259.342.16.?, $\ldots$ |
$[]$ |
| 1225.d2 |
1225f1 |
1225.d |
1225f |
$2$ |
$37$ |
\( 5^{2} \cdot 7^{2} \) |
\( - 5^{3} \cdot 7^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$37$ |
37.114.4.1 |
37B.8.1 |
$5180$ |
$2736$ |
$97$ |
$1$ |
$1$ |
|
$0$ |
$336$ |
$0.437981$ |
$-9317$ |
$0.80290$ |
$4.17756$ |
$[1, 0, 0, -393, -3298]$ |
\(y^2+xy=x^3-393x-3298\) |
20.2.0.a.1, 37.114.4.b.1, 148.228.10.?, 185.456.10.?, 259.342.16.?, $\ldots$ |
$[]$ |
| 1225.e1 |
1225a3 |
1225.e |
1225a |
$3$ |
$9$ |
\( 5^{2} \cdot 7^{2} \) |
\( - 5^{15} \cdot 7^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.12.0.1 |
3B |
$630$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$6912$ |
$1.905136$ |
$-250523582464/13671875$ |
$1.02112$ |
$6.70385$ |
$[0, 1, 1, -160883, 25929019]$ |
\(y^2+y=x^3+x^2-160883x+25929019\) |
3.4.0.a.1, 6.8.0-3.a.1.2, 9.12.0.a.1, 18.24.0-9.a.1.2, 63.36.0.e.2, $\ldots$ |
$[]$ |
| 1225.e2 |
1225a1 |
1225.e |
1225a |
$3$ |
$9$ |
\( 5^{2} \cdot 7^{2} \) |
\( - 5^{7} \cdot 7^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.12.0.1 |
3B |
$630$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$768$ |
$0.806524$ |
$-262144/35$ |
$0.88715$ |
$4.78383$ |
$[0, 1, 1, -1633, -28731]$ |
\(y^2+y=x^3+x^2-1633x-28731\) |
3.4.0.a.1, 6.8.0-3.a.1.1, 9.12.0.a.1, 18.24.0-9.a.1.1, 63.36.0.e.1, $\ldots$ |
$[]$ |
| 1225.e3 |
1225a2 |
1225.e |
1225a |
$3$ |
$9$ |
\( 5^{2} \cdot 7^{2} \) |
\( - 5^{9} \cdot 7^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.12.0.1 |
3Cs |
$630$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$2304$ |
$1.355829$ |
$71991296/42875$ |
$1.06493$ |
$5.54434$ |
$[0, 1, 1, 10617, 75394]$ |
\(y^2+y=x^3+x^2+10617x+75394\) |
3.12.0.a.1, 6.24.0-3.a.1.1, 63.36.0.b.1, 70.2.0.a.1, 105.24.0.?, $\ldots$ |
$[]$ |
| 1225.f1 |
1225e2 |
1225.f |
1225e |
$2$ |
$37$ |
\( 5^{2} \cdot 7^{2} \) |
\( - 5^{9} \cdot 7^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$37$ |
37.114.4.2 |
37B.8.2 |
$5180$ |
$2736$ |
$97$ |
$1$ |
$1$ |
|
$0$ |
$62160$ |
$3.048161$ |
$-162677523113838677$ |
$1.07344$ |
$9.79971$ |
$[1, 1, 0, -254901700, 1566310159625]$ |
\(y^2+xy=x^3+x^2-254901700x+1566310159625\) |
20.2.0.a.1, 37.114.4.b.2, 148.228.10.?, 185.456.10.?, 259.342.16.?, $\ldots$ |
$[]$ |
| 1225.f2 |
1225e1 |
1225.f |
1225e |
$2$ |
$37$ |
\( 5^{2} \cdot 7^{2} \) |
\( - 5^{9} \cdot 7^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$37$ |
37.114.4.1 |
37B.8.1 |
$5180$ |
$2736$ |
$97$ |
$1$ |
$1$ |
|
$0$ |
$1680$ |
$1.242701$ |
$-9317$ |
$0.80290$ |
$5.53560$ |
$[1, 1, 0, -9825, -412250]$ |
\(y^2+xy=x^3+x^2-9825x-412250\) |
20.2.0.a.1, 37.114.4.b.1, 148.228.10.?, 185.456.10.?, 259.342.16.?, $\ldots$ |
$[]$ |
| 1225.g1 |
1225g2 |
1225.g |
1225g |
$2$ |
$37$ |
\( 5^{2} \cdot 7^{2} \) |
\( - 5^{9} \cdot 7^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$37$ |
37.114.4.2 |
37B.8.2 |
$5180$ |
$2736$ |
$97$ |
$34.79035741$ |
$1$ |
|
$0$ |
$8880$ |
$2.075203$ |
$-162677523113838677$ |
$1.07344$ |
$8.15775$ |
$[1, 0, 1, -5202076, -4567245077]$ |
\(y^2+xy+y=x^3-5202076x-4567245077\) |
20.2.0.a.1, 37.114.4.b.2, 148.228.10.?, 185.228.10.?, 259.342.16.?, $\ldots$ |
$[(14222544712537937/344191, 1693402407380764960626706/344191)]$ |
| 1225.g2 |
1225g1 |
1225.g |
1225g |
$2$ |
$37$ |
\( 5^{2} \cdot 7^{2} \) |
\( - 5^{9} \cdot 7^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$37$ |
37.114.4.1 |
37B.8.1 |
$5180$ |
$2736$ |
$97$ |
$0.940279930$ |
$1$ |
|
$2$ |
$240$ |
$0.269745$ |
$-9317$ |
$0.80290$ |
$3.89364$ |
$[1, 0, 1, -201, 1173]$ |
\(y^2+xy+y=x^3-201x+1173\) |
20.2.0.a.1, 37.114.4.b.1, 148.228.10.?, 185.228.10.?, 259.342.16.?, $\ldots$ |
$[(27, 111)]$ |
| 1225.h1 |
1225d1 |
1225.h |
1225d |
$1$ |
$1$ |
\( 5^{2} \cdot 7^{2} \) |
\( - 5^{9} \cdot 7^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.3.0.1 |
3Nn |
$210$ |
$12$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$8064$ |
$1.360912$ |
$-110592/125$ |
$0.98030$ |
$5.60652$ |
$[0, 0, 1, -8575, -525219]$ |
\(y^2+y=x^3-8575x-525219\) |
3.3.0.a.1, 21.6.0.a.1, 30.6.0.c.1, 70.2.0.a.1, 210.12.1.? |
$[]$ |
| 1225.i1 |
1225i2 |
1225.i |
1225i |
$2$ |
$5$ |
\( 5^{2} \cdot 7^{2} \) |
\( - 5^{9} \cdot 7^{11} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.12.0.1 |
5B.4.1 |
$70$ |
$48$ |
$1$ |
$8.564033026$ |
$1$ |
|
$0$ |
$9600$ |
$1.831867$ |
$-2887553024/16807$ |
$0.98803$ |
$6.74394$ |
$[0, -1, 1, -181708, -29902307]$ |
\(y^2+y=x^3-x^2-181708x-29902307\) |
5.12.0.a.1, 10.24.0-5.a.1.1, 35.24.0-5.a.1.1, 70.48.1-70.d.1.1 |
$[(409093/2, 261653871/2)]$ |
| 1225.i2 |
1225i1 |
1225.i |
1225i |
$2$ |
$5$ |
\( 5^{2} \cdot 7^{2} \) |
\( - 5^{9} \cdot 7^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.12.0.2 |
5B.4.2 |
$70$ |
$48$ |
$1$ |
$1.712806605$ |
$1$ |
|
$0$ |
$1920$ |
$1.027147$ |
$4096/7$ |
$0.98030$ |
$4.94292$ |
$[0, -1, 1, 2042, 48943]$ |
\(y^2+y=x^3-x^2+2042x+48943\) |
5.12.0.a.2, 10.24.0-5.a.2.2, 35.24.0-5.a.2.1, 70.48.1-70.d.2.1 |
$[(293/2, 6121/2)]$ |
| 1225.j1 |
1225c1 |
1225.j |
1225c |
$1$ |
$1$ |
\( 5^{2} \cdot 7^{2} \) |
\( - 5^{9} \cdot 7^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.3.0.1 |
3Nn |
$210$ |
$12$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$1152$ |
$0.387958$ |
$-110592/125$ |
$0.98030$ |
$3.96457$ |
$[0, 0, 1, -175, 1531]$ |
\(y^2+y=x^3-175x+1531\) |
3.3.0.a.1, 21.6.0.a.1, 30.6.0.c.1, 70.2.0.a.1, 210.12.1.? |
$[]$ |
