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 |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
784.a1 |
784b1 |
784.a |
784b |
$1$ |
$1$ |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
4.4.0.2 |
2Cn |
$28$ |
$12$ |
$0$ |
$0.258432387$ |
$1$ |
|
$4$ |
$336$ |
$0.318593$ |
$48384$ |
$[0, 0, 0, -343, 2401]$ |
\(y^2=x^3-343x+2401\) |
2.2.0.a.1, 4.4.0-2.a.1.1, 14.6.0.a.1, 28.12.0-14.a.1.3 |
$[(0, 49)]$ |
784.b1 |
784j6 |
784.b |
784j |
$6$ |
$18$ |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{21} \cdot 7^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.6, 9.12.0.1 |
2B, 3B |
$504$ |
$864$ |
$21$ |
$7.014414334$ |
$1$ |
|
$1$ |
$6912$ |
$2.079205$ |
$2251439055699625/25088$ |
$[0, 1, 0, -2140728, -1206278060]$ |
\(y^2=x^3+x^2-2140728x-1206278060\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 9.12.0.a.1, $\ldots$ |
$[(33604/3, 5590214/3)]$ |
784.b2 |
784j5 |
784.b |
784j |
$6$ |
$18$ |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{30} \cdot 7^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.1, 9.12.0.1 |
2B, 3B |
$504$ |
$864$ |
$21$ |
$3.507207167$ |
$1$ |
|
$3$ |
$3456$ |
$1.732630$ |
$-548347731625/1835008$ |
$[0, 1, 0, -133688, -18913196]$ |
\(y^2=x^3+x^2-133688x-18913196\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.c.1, 9.12.0.a.1, $\ldots$ |
$[(548, 8526)]$ |
784.b3 |
784j4 |
784.b |
784j |
$6$ |
$18$ |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{15} \cdot 7^{12} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.6, 3.12.0.1 |
2B, 3Cs |
$504$ |
$864$ |
$21$ |
$2.338138111$ |
$1$ |
|
$3$ |
$2304$ |
$1.529898$ |
$4956477625/941192$ |
$[0, 1, 0, -27848, -1475468]$ |
\(y^2=x^3+x^2-27848x-1475468\) |
2.3.0.a.1, 3.12.0.a.1, 6.36.0.a.1, 8.6.0.b.1, 12.72.0-6.a.1.2, $\ldots$ |
$[(-124, 294)]$ |
784.b4 |
784j2 |
784.b |
784j |
$6$ |
$18$ |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{13} \cdot 7^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.6, 9.12.0.1 |
2B, 3B |
$504$ |
$864$ |
$21$ |
$0.779379370$ |
$1$ |
|
$7$ |
$768$ |
$0.980591$ |
$128787625/98$ |
$[0, 1, 0, -8248, 285396]$ |
\(y^2=x^3+x^2-8248x+285396\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 9.12.0.a.1, $\ldots$ |
$[(44, 98)]$ |
784.b5 |
784j1 |
784.b |
784j |
$6$ |
$18$ |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{14} \cdot 7^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.1, 9.12.0.1 |
2B, 3B |
$504$ |
$864$ |
$21$ |
$0.389689685$ |
$1$ |
|
$9$ |
$384$ |
$0.634017$ |
$-15625/28$ |
$[0, 1, 0, -408, 6292]$ |
\(y^2=x^3+x^2-408x+6292\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.c.1, 9.12.0.a.1, $\ldots$ |
$[(-12, 98)]$ |
784.b6 |
784j3 |
784.b |
784j |
$6$ |
$18$ |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{18} \cdot 7^{9} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.1, 3.12.0.1 |
2B, 3Cs |
$504$ |
$864$ |
$21$ |
$1.169069055$ |
$1$ |
|
$5$ |
$1152$ |
$1.183323$ |
$9938375/21952$ |
$[0, 1, 0, 3512, -133260]$ |
\(y^2=x^3+x^2+3512x-133260\) |
2.3.0.a.1, 3.12.0.a.1, 6.36.0.a.1, 8.6.0.c.1, 12.72.0-6.a.1.4, $\ldots$ |
$[(156, 2058)]$ |
784.c1 |
784d1 |
784.c |
784d |
$1$ |
$1$ |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
2.2.0.1 |
2Cn |
$28$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$336$ |
$0.596082$ |
$12544$ |
$[0, -1, 0, -800, 8359]$ |
\(y^2=x^3-x^2-800x+8359\) |
2.2.0.a.1, 14.6.0.a.1, 28.12.0-14.a.1.1 |
$[]$ |
784.d1 |
784g2 |
784.d |
784g |
$2$ |
$3$ |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 3$ |
4.4.0.2, 9.12.0.2 |
2Cn, 3B |
$252$ |
$864$ |
$28$ |
$1$ |
$1$ |
|
$0$ |
$504$ |
$0.767920$ |
$406749952$ |
$[0, -1, 0, -6974, 226507]$ |
\(y^2=x^3-x^2-6974x+226507\) |
2.2.0.a.1, 3.4.0.a.1, 4.4.0-2.a.1.1, 6.8.0.a.1, 9.12.0.b.1, $\ldots$ |
$[]$ |
784.d2 |
784g1 |
784.d |
784g |
$2$ |
$3$ |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 3$ |
4.4.0.2, 9.12.0.2 |
2Cn, 3B |
$252$ |
$864$ |
$28$ |
$1$ |
$1$ |
|
$0$ |
$168$ |
$0.218614$ |
$1792$ |
$[0, -1, 0, -114, 127]$ |
\(y^2=x^3-x^2-114x+127\) |
2.2.0.a.1, 3.4.0.a.1, 4.4.0-2.a.1.1, 6.8.0.a.1, 9.12.0.b.1, $\ldots$ |
$[]$ |
784.e1 |
784c4 |
784.e |
784c |
$4$ |
$4$ |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{11} \cdot 7^{7} \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.51 |
2B |
$56$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$768$ |
$0.970922$ |
$1443468546/7$ |
$[0, 0, 0, -14651, 682570]$ |
\(y^2=x^3-14651x+682570\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.p.1.8, 56.48.0-56.bp.1.4 |
$[]$ |
784.e2 |
784c3 |
784.e |
784c |
$4$ |
$4$ |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{11} \cdot 7^{10} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.105 |
2B |
$56$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$768$ |
$0.970922$ |
$11090466/2401$ |
$[0, 0, 0, -2891, -47334]$ |
\(y^2=x^3-2891x-47334\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.k.1.3, 28.12.0-4.c.1.2, 56.48.0-56.v.1.7 |
$[]$ |
784.e3 |
784c2 |
784.e |
784c |
$4$ |
$4$ |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{10} \cdot 7^{8} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.5 |
2Cs |
$56$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$384$ |
$0.624349$ |
$740772/49$ |
$[0, 0, 0, -931, 10290]$ |
\(y^2=x^3-931x+10290\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.a.1.3, 28.24.0-28.b.1.2, 56.48.0-56.d.1.4 |
$[]$ |
784.e4 |
784c1 |
784.e |
784c |
$4$ |
$4$ |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{8} \cdot 7^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.61 |
2B |
$56$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$192$ |
$0.277775$ |
$432/7$ |
$[0, 0, 0, 49, 686]$ |
\(y^2=x^3+49x+686\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.p.1.6, 14.6.0.b.1, 28.24.0-28.g.1.1, $\ldots$ |
$[]$ |
784.f1 |
784h4 |
784.f |
784h |
$4$ |
$14$ |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{9} \) |
$1$ |
$\Z/2\Z$ |
$\Q(\sqrt{-7})$ |
$-28$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$6.042134670$ |
$1$ |
|
$3$ |
$896$ |
$1.213537$ |
$16581375$ |
$[0, 0, 0, -29155, -1915998]$ |
\(y^2=x^3-29155x-1915998\) |
|
$[(743, 19662)]$ |
784.f2 |
784h3 |
784.f |
784h |
$4$ |
$14$ |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{12} \cdot 7^{9} \) |
$1$ |
$\Z/2\Z$ |
$\Q(\sqrt{-7})$ |
$-7$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$3.021067335$ |
$1$ |
|
$5$ |
$448$ |
$0.866964$ |
$-3375$ |
$[0, 0, 0, -1715, -33614]$ |
\(y^2=x^3-1715x-33614\) |
|
$[(57, 232)]$ |
784.f3 |
784h2 |
784.f |
784h |
$4$ |
$14$ |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{3} \) |
$1$ |
$\Z/2\Z$ |
$\Q(\sqrt{-7})$ |
$-28$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$0.863162095$ |
$1$ |
|
$5$ |
$128$ |
$0.240582$ |
$16581375$ |
$[0, 0, 0, -595, 5586]$ |
\(y^2=x^3-595x+5586\) |
|
$[(7, 42)]$ |
784.f4 |
784h1 |
784.f |
784h |
$4$ |
$14$ |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{12} \cdot 7^{3} \) |
$1$ |
$\Z/2\Z$ |
$\Q(\sqrt{-7})$ |
$-7$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$0.431581047$ |
$1$ |
|
$9$ |
$64$ |
$-0.105991$ |
$-3375$ |
$[0, 0, 0, -35, 98]$ |
\(y^2=x^3-35x+98\) |
|
$[(1, 8)]$ |
784.g1 |
784i2 |
784.g |
784i |
$2$ |
$3$ |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 3$ |
2.2.0.1, 9.12.0.2 |
2Cn, 3B |
$252$ |
$864$ |
$28$ |
$1.656005557$ |
$1$ |
|
$0$ |
$72$ |
$-0.205035$ |
$406749952$ |
$[0, 1, 0, -142, -701]$ |
\(y^2=x^3+x^2-142x-701\) |
2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 9.12.0.b.1, 12.16.0.a.1, $\ldots$ |
$[(-65/3, 1/3)]$ |
784.g2 |
784i1 |
784.g |
784i |
$2$ |
$3$ |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 3$ |
2.2.0.1, 9.12.0.2 |
2Cn, 3B |
$252$ |
$864$ |
$28$ |
$0.552001852$ |
$1$ |
|
$2$ |
$24$ |
$-0.754341$ |
$1792$ |
$[0, 1, 0, -2, -1]$ |
\(y^2=x^3+x^2-2x-1\) |
2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 9.12.0.b.1, 12.16.0.a.2, $\ldots$ |
$[(-1, 1)]$ |
784.h1 |
784a1 |
784.h |
784a |
$1$ |
$1$ |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{4} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
4.4.0.2 |
2Cn |
$28$ |
$12$ |
$0$ |
$1.004255008$ |
$1$ |
|
$2$ |
$48$ |
$-0.376873$ |
$12544$ |
$[0, 1, 0, -16, -29]$ |
\(y^2=x^3+x^2-16x-29\) |
2.2.0.a.1, 4.4.0-2.a.1.1, 14.6.0.a.1, 28.12.0-14.a.1.3 |
$[(-3, 1)]$ |
784.i1 |
784e2 |
784.i |
784e |
$2$ |
$2$ |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{11} \cdot 7^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.6 |
2B |
$56$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$768$ |
$0.738286$ |
$3543122/49$ |
$[0, -1, 0, -1976, -32752]$ |
\(y^2=x^3-x^2-1976x-32752\) |
2.3.0.a.1, 8.6.0.b.1, 28.6.0.c.1, 56.12.0.k.1 |
$[]$ |
784.i2 |
784e1 |
784.i |
784e |
$2$ |
$2$ |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{10} \cdot 7^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.1 |
2B |
$56$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$384$ |
$0.391713$ |
$-4/7$ |
$[0, -1, 0, -16, -1392]$ |
\(y^2=x^3-x^2-16x-1392\) |
2.3.0.a.1, 8.6.0.c.1, 14.6.0.b.1, 56.12.0.n.1 |
$[]$ |
784.j1 |
784f1 |
784.j |
784f |
$1$ |
$1$ |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
2.2.0.1 |
2Cn |
$28$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$48$ |
$-0.654362$ |
$48384$ |
$[0, 0, 0, -7, -7]$ |
\(y^2=x^3-7x-7\) |
2.2.0.a.1, 14.6.0.a.1, 28.12.0-14.a.1.1 |
$[]$ |