| 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 |
| 441.a1 |
441f2 |
441.a |
441f |
$2$ |
$13$ |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{19} \cdot 7^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$13$ |
13.28.0.2 |
13B.4.2 |
$546$ |
$336$ |
$9$ |
$0.991510447$ |
$1$ |
|
$4$ |
$624$ |
$0.986693$ |
$-1713910976512/1594323$ |
$1.10592$ |
$6.34827$ |
$[0, 0, 1, -8211, -286610]$ |
\(y^2+y=x^3-8211x-286610\) |
6.2.0.a.1, 13.28.0.a.2, 78.56.1.?, 91.84.2.?, 182.168.2.?, $\ldots$ |
$[(235, 3280)]$ |
| 441.a2 |
441f1 |
441.a |
441f |
$2$ |
$13$ |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{7} \cdot 7^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$13$ |
13.28.0.1 |
13B.4.1 |
$546$ |
$336$ |
$9$ |
$0.076270034$ |
$1$ |
|
$10$ |
$48$ |
$-0.295781$ |
$-28672/3$ |
$0.91239$ |
$3.43459$ |
$[0, 0, 1, -21, 40]$ |
\(y^2+y=x^3-21x+40\) |
6.2.0.a.1, 13.28.0.a.1, 78.56.1.?, 91.84.2.?, 182.168.2.?, $\ldots$ |
$[(4, 4)]$ |
| 441.b1 |
441e2 |
441.b |
441e |
$2$ |
$13$ |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{19} \cdot 7^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$13$ |
13.28.0.2 |
13B.4.2 |
$546$ |
$336$ |
$9$ |
$1$ |
$1$ |
|
$0$ |
$4368$ |
$1.959648$ |
$-1713910976512/1594323$ |
$1.10592$ |
$8.26572$ |
$[0, 0, 1, -402339, 98307144]$ |
\(y^2+y=x^3-402339x+98307144\) |
6.2.0.a.1, 13.28.0.a.2, 26.56.0-13.a.2.2, 39.56.0-13.a.2.1, 78.112.1.?, $\ldots$ |
$[]$ |
| 441.b2 |
441e1 |
441.b |
441e |
$2$ |
$13$ |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{7} \cdot 7^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$13$ |
13.28.0.1 |
13B.4.1 |
$546$ |
$336$ |
$9$ |
$1$ |
$1$ |
|
$0$ |
$336$ |
$0.677174$ |
$-28672/3$ |
$0.91239$ |
$5.35204$ |
$[0, 0, 1, -1029, -13806]$ |
\(y^2+y=x^3-1029x-13806\) |
6.2.0.a.1, 13.28.0.a.1, 26.56.0-13.a.1.1, 39.56.0-13.a.1.1, 78.112.1.?, $\ldots$ |
$[]$ |
| 441.c1 |
441d4 |
441.c |
441d |
$4$ |
$14$ |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{6} \cdot 7^{9} \) |
$1$ |
$\Z/2\Z$ |
$\Q(\sqrt{-7})$ |
$-28$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1.534261868$ |
$1$ |
|
$6$ |
$448$ |
$1.069696$ |
$16581375$ |
$1.19804$ |
$6.68884$ |
$[1, -1, 1, -16400, -804212]$ |
\(y^2+xy+y=x^3-x^2-16400x-804212\) |
|
$[(-74, 41)]$ |
| 441.c2 |
441d3 |
441.c |
441d |
$4$ |
$14$ |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{6} \cdot 7^{9} \) |
$1$ |
$\Z/2\Z$ |
$\Q(\sqrt{-7})$ |
$-7$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$3.068523736$ |
$1$ |
|
$5$ |
$224$ |
$0.723123$ |
$-3375$ |
$0.98030$ |
$5.36085$ |
$[1, -1, 1, -965, -13940]$ |
\(y^2+xy+y=x^3-x^2-965x-13940\) |
|
$[(46, 170)]$ |
| 441.c3 |
441d2 |
441.c |
441d |
$4$ |
$14$ |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{6} \cdot 7^{3} \) |
$1$ |
$\Z/2\Z$ |
$\Q(\sqrt{-7})$ |
$-28$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$0.219180266$ |
$1$ |
|
$12$ |
$64$ |
$0.096741$ |
$16581375$ |
$1.19804$ |
$4.77139$ |
$[1, -1, 1, -335, 2440]$ |
\(y^2+xy+y=x^3-x^2-335x+2440\) |
|
$[(16, 23)]$ |
| 441.c4 |
441d1 |
441.c |
441d |
$4$ |
$14$ |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{6} \cdot 7^{3} \) |
$1$ |
$\Z/2\Z$ |
$\Q(\sqrt{-7})$ |
$-7$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$0.438360533$ |
$1$ |
|
$7$ |
$32$ |
$-0.249832$ |
$-3375$ |
$0.98030$ |
$3.44340$ |
$[1, -1, 1, -20, 46]$ |
\(y^2+xy+y=x^3-x^2-20x+46\) |
|
$[(2, 2)]$ |
| 441.d1 |
441b2 |
441.d |
441b |
$2$ |
$3$ |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{9} \cdot 7^{4} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3, 7$ |
27.648.18.4, 7.84.1.1 |
3B.1.2, 7Ns.6.1.2 |
|
|
|
$0.298091926$ |
$1$ |
|
$6$ |
$72$ |
$0.151479$ |
$0$ |
|
$4.12641$ |
$[0, 0, 1, 0, -331]$ |
\(y^2+y=x^3-331\) |
|
$[(21, 94)]$ |
| 441.d2 |
441b1 |
441.d |
441b |
$2$ |
$3$ |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{3} \cdot 7^{4} \) |
$1$ |
$\Z/3\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3, 7$ |
27.648.18.1, 7.84.1.1 |
3B.1.1, 7Ns.6.1.2 |
|
|
|
$0.894275780$ |
$1$ |
|
$6$ |
$24$ |
$-0.397828$ |
$0$ |
|
$3.04386$ |
$[0, 0, 1, 0, 12]$ |
\(y^2+y=x^3+12\) |
|
$[(2, 4)]$ |
| 441.e1 |
441a1 |
441.e |
441a |
$2$ |
$3$ |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{3} \cdot 7^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$7$ |
7.84.1.1 |
7Ns.6.1.2 |
|
|
|
$1$ |
$1$ |
|
$0$ |
$168$ |
$0.575128$ |
$0$ |
|
$4.96131$ |
$[0, 0, 1, 0, -4202]$ |
\(y^2+y=x^3-4202\) |
|
$[]$ |
| 441.e2 |
441a2 |
441.e |
441a |
$2$ |
$3$ |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{9} \cdot 7^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$7$ |
7.84.1.1 |
7Ns.6.1.2 |
|
|
|
$1$ |
$1$ |
|
$0$ |
$504$ |
$1.124434$ |
$0$ |
|
$6.04386$ |
$[0, 0, 1, 0, 113447]$ |
\(y^2+y=x^3+113447\) |
|
$[]$ |
| 441.f1 |
441c5 |
441.f |
441c |
$6$ |
$8$ |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{7} \cdot 7^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.119 |
2B |
$336$ |
$192$ |
$1$ |
$10.55403529$ |
$1$ |
|
$0$ |
$1536$ |
$1.596466$ |
$53297461115137/147$ |
$1.05087$ |
$8.19078$ |
$[1, -1, 0, -345753, -78165914]$ |
\(y^2+xy=x^3-x^2-345753x-78165914\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.7, 12.12.0.h.1, 16.48.0-16.e.2.16, $\ldots$ |
$[(234399/10, 108307823/10)]$ |
| 441.f2 |
441c3 |
441.f |
441c |
$6$ |
$8$ |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{10} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.113 |
2Cs |
$168$ |
$192$ |
$1$ |
$5.277017646$ |
$1$ |
|
$2$ |
$768$ |
$1.249893$ |
$13027640977/21609$ |
$1.08149$ |
$6.82496$ |
$[1, -1, 0, -21618, -1216265]$ |
\(y^2+xy=x^3-x^2-21618x-1216265\) |
2.6.0.a.1, 4.12.0.b.1, 8.48.0-8.e.1.15, 12.24.0.c.1, 24.96.0-24.j.2.10, $\ldots$ |
$[(9255/2, 879115/2)]$ |
| 441.f3 |
441c4 |
441.f |
441c |
$6$ |
$8$ |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{14} \cdot 7^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.99 |
2B |
$336$ |
$192$ |
$1$ |
$1.319254411$ |
$1$ |
|
$4$ |
$768$ |
$1.249893$ |
$6570725617/45927$ |
$1.00160$ |
$6.71255$ |
$[1, -1, 0, -17208, 867901]$ |
\(y^2+xy=x^3-x^2-17208x+867901\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 12.12.0-4.c.1.1, 16.48.0-8.bb.1.3, $\ldots$ |
$[(20, 719)]$ |
| 441.f4 |
441c6 |
441.f |
441c |
$6$ |
$8$ |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{7} \cdot 7^{14} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.131 |
2B |
$336$ |
$192$ |
$1$ |
$2.638508823$ |
$1$ |
|
$2$ |
$1536$ |
$1.596466$ |
$-4354703137/17294403$ |
$1.04266$ |
$6.98365$ |
$[1, -1, 0, -15003, -1979636]$ |
\(y^2+xy=x^3-x^2-15003x-1979636\) |
2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 8.24.0.bb.2, 12.12.0.g.1, $\ldots$ |
$[(296, 4262)]$ |
| 441.f5 |
441c2 |
441.f |
441c |
$6$ |
$8$ |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{10} \cdot 7^{8} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.65 |
2Cs |
$168$ |
$192$ |
$1$ |
$2.638508823$ |
$1$ |
|
$6$ |
$384$ |
$0.903319$ |
$7189057/3969$ |
$1.14862$ |
$5.59286$ |
$[1, -1, 0, -1773, -5720]$ |
\(y^2+xy=x^3-x^2-1773x-5720\) |
2.6.0.a.1, 4.12.0.b.1, 8.48.0-8.e.2.11, 12.24.0-4.b.1.2, 24.96.0-24.w.2.12, $\ldots$ |
$[(-4, 38)]$ |
| 441.f6 |
441c1 |
441.f |
441c |
$6$ |
$8$ |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{8} \cdot 7^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.85 |
2B |
$336$ |
$192$ |
$1$ |
$1.319254411$ |
$1$ |
|
$5$ |
$192$ |
$0.556746$ |
$103823/63$ |
$0.97868$ |
$4.89692$ |
$[1, -1, 0, 432, -869]$ |
\(y^2+xy=x^3-x^2+432x-869\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.1, 12.12.0-4.c.1.2, 14.6.0.b.1, $\ldots$ |
$[(30, 181)]$ |
