| 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 |
| 12996.a1 |
12996i1 |
12996.a |
12996i |
$1$ |
$1$ |
\( 2^{2} \cdot 3^{2} \cdot 19^{2} \) |
\( - 2^{4} \cdot 3^{9} \cdot 19^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 5$ |
4.4.0.1, 5.5.0.1 |
5S4 |
$60$ |
$40$ |
$2$ |
$0.233482257$ |
$1$ |
|
$8$ |
$20736$ |
$0.873631$ |
$-1815478272$ |
$1.37833$ |
$4.20892$ |
$[0, 0, 0, -12312, 525825]$ |
\(y^2=x^3-12312x+525825\) |
4.4.0.a.1, 5.5.0.a.1, 6.2.0.a.1, 12.8.0.c.1, 20.20.1.c.1, $\ldots$ |
$[(66, 27)]$ |
| 12996.b1 |
12996d1 |
12996.b |
12996d |
$1$ |
$1$ |
\( 2^{2} \cdot 3^{2} \cdot 19^{2} \) |
\( - 2^{4} \cdot 3^{9} \cdot 19^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 5$ |
4.4.0.1, 5.5.0.1 |
5S4 |
$60$ |
$40$ |
$2$ |
$1$ |
$1$ |
|
$0$ |
$393984$ |
$2.345848$ |
$-1815478272$ |
$1.37833$ |
$6.07399$ |
$[0, 0, 0, -4444632, -3606633675]$ |
\(y^2=x^3-4444632x-3606633675\) |
4.4.0.a.1, 5.5.0.a.1, 6.2.0.a.1, 12.8.0.c.1, 20.20.1.c.1, $\ldots$ |
$[ ]$ |
| 12996.c1 |
12996o2 |
12996.c |
12996o |
$2$ |
$2$ |
\( 2^{2} \cdot 3^{2} \cdot 19^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 19^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$228$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$103680$ |
$2.044083$ |
$340062928/13851$ |
$0.89938$ |
$5.22023$ |
$[0, 0, 0, -299991, 60976510]$ |
\(y^2=x^3-299991x+60976510\) |
2.3.0.a.1, 12.6.0.c.1, 76.6.0.?, 228.12.0.? |
$[ ]$ |
| 12996.c2 |
12996o1 |
12996.c |
12996o |
$2$ |
$2$ |
\( 2^{2} \cdot 3^{2} \cdot 19^{2} \) |
\( - 2^{4} \cdot 3^{9} \cdot 19^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$228$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$51840$ |
$1.697508$ |
$131072/9747$ |
$1.13743$ |
$4.60945$ |
$[0, 0, 0, 8664, 3504949]$ |
\(y^2=x^3+8664x+3504949\) |
2.3.0.a.1, 6.6.0.a.1, 76.6.0.?, 228.12.0.? |
$[ ]$ |
| 12996.d1 |
12996f4 |
12996.d |
12996f |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \cdot 19^{2} \) |
\( 2^{8} \cdot 3^{9} \cdot 19^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q(\sqrt{-3})$ |
$-12$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$2.290307121$ |
$1$ |
|
$5$ |
$36288$ |
$1.552685$ |
$54000$ |
$1.02720$ |
$4.64466$ |
$[0, 0, 0, -48735, 4074246]$ |
\(y^2=x^3-48735x+4074246\) |
|
$[(87, 702)]$ |
| 12996.d2 |
12996f2 |
12996.d |
12996f |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \cdot 19^{2} \) |
\( 2^{8} \cdot 3^{3} \cdot 19^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q(\sqrt{-3})$ |
$-12$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$6.870921363$ |
$1$ |
|
$1$ |
$12096$ |
$1.003378$ |
$54000$ |
$1.02720$ |
$3.94878$ |
$[0, 0, 0, -5415, -150898]$ |
\(y^2=x^3-5415x-150898\) |
|
$[(-2294/7, 468/7)]$ |
| 12996.d3 |
12996f1 |
12996.d |
12996f |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \cdot 19^{2} \) |
\( - 2^{4} \cdot 3^{3} \cdot 19^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$2$ |
16.192.9.83 |
2B |
|
|
|
$3.435460681$ |
$1$ |
|
$1$ |
$6048$ |
$0.656804$ |
$0$ |
|
$3.29270$ |
$[0, 0, 0, 0, -6859]$ |
\(y^2=x^3-6859\) |
|
$[(475/3, 10108/3)]$ |
| 12996.d4 |
12996f3 |
12996.d |
12996f |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \cdot 19^{2} \) |
\( - 2^{4} \cdot 3^{9} \cdot 19^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$2$ |
16.192.9.83 |
2B |
|
|
|
$1.145153560$ |
$1$ |
|
$7$ |
$18144$ |
$1.206110$ |
$0$ |
|
$3.98858$ |
$[0, 0, 0, 0, 185193]$ |
\(y^2=x^3+185193\) |
|
$[(-38, 361)]$ |
| 12996.e1 |
12996a2 |
12996.e |
12996a |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{2} \cdot 19^{2} \) |
\( - 2^{4} \cdot 3^{9} \cdot 19^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.4 |
3B.1.2 |
|
|
|
$1$ |
$1$ |
|
$0$ |
$49248$ |
$1.696850$ |
$0$ |
|
$4.61027$ |
$[0, 0, 0, 0, -3518667]$ |
\(y^2=x^3-3518667\) |
|
$[ ]$ |
| 12996.e2 |
12996a1 |
12996.e |
12996a |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{2} \cdot 19^{2} \) |
\( - 2^{4} \cdot 3^{3} \cdot 19^{8} \) |
$0$ |
$\Z/3\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.1 |
3B.1.1 |
|
|
|
$1$ |
$1$ |
|
$2$ |
$16416$ |
$1.147545$ |
$0$ |
|
$3.91439$ |
$[0, 0, 0, 0, 130321]$ |
\(y^2=x^3+130321\) |
|
$[ ]$ |
| 12996.f1 |
12996e1 |
12996.f |
12996e |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{2} \cdot 19^{2} \) |
\( - 2^{4} \cdot 3^{3} \cdot 19^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1.625412405$ |
$1$ |
|
$2$ |
$864$ |
$-0.324676$ |
$0$ |
|
$2.04933$ |
$[0, 0, 0, 0, -19]$ |
\(y^2=x^3-19\) |
|
$[(7, 18)]$ |
| 12996.f2 |
12996e2 |
12996.f |
12996e |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{2} \cdot 19^{2} \) |
\( - 2^{4} \cdot 3^{9} \cdot 19^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$0.541804135$ |
$1$ |
|
$6$ |
$2592$ |
$0.224631$ |
$0$ |
|
$2.74521$ |
$[0, 0, 0, 0, 513]$ |
\(y^2=x^3+513\) |
|
$[(6, 27)]$ |
| 12996.g1 |
12996g1 |
12996.g |
12996g |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{2} \cdot 19^{2} \) |
\( - 2^{4} \cdot 3^{3} \cdot 19^{10} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$13.07949166$ |
$1$ |
|
$0$ |
$65664$ |
$1.638285$ |
$0$ |
|
$4.53608$ |
$[0, 0, 0, 0, -2476099]$ |
\(y^2=x^3-2476099\) |
|
$[(825595/7, 750154068/7)]$ |
| 12996.g2 |
12996g2 |
12996.g |
12996g |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{2} \cdot 19^{2} \) |
\( - 2^{4} \cdot 3^{9} \cdot 19^{10} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$4.359830555$ |
$1$ |
|
$2$ |
$196992$ |
$2.187592$ |
$0$ |
|
$5.23196$ |
$[0, 0, 0, 0, 66854673]$ |
\(y^2=x^3+66854673\) |
|
$[(42, 8181)]$ |
| 12996.h1 |
12996b2 |
12996.h |
12996b |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{2} \cdot 19^{2} \) |
\( - 2^{4} \cdot 3^{9} \cdot 19^{4} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.4 |
3B.1.2 |
|
|
|
$1$ |
$1$ |
|
$0$ |
$10368$ |
$0.715370$ |
$0$ |
|
$3.36690$ |
$[0, 0, 0, 0, -9747]$ |
\(y^2=x^3-9747\) |
|
$[ ]$ |
| 12996.h2 |
12996b1 |
12996.h |
12996b |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{2} \cdot 19^{2} \) |
\( - 2^{4} \cdot 3^{3} \cdot 19^{4} \) |
$0$ |
$\Z/3\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.1 |
3B.1.1 |
|
|
|
$1$ |
$1$ |
|
$2$ |
$3456$ |
$0.166064$ |
$0$ |
|
$2.67101$ |
$[0, 0, 0, 0, 361]$ |
\(y^2=x^3+361\) |
|
$[ ]$ |
| 12996.i1 |
12996n1 |
12996.i |
12996n |
$1$ |
$1$ |
\( 2^{2} \cdot 3^{2} \cdot 19^{2} \) |
\( - 2^{8} \cdot 3^{6} \cdot 19^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$38$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$51840$ |
$1.580595$ |
$-4194304/19$ |
$1.07903$ |
$4.75703$ |
$[0, 0, 0, -69312, -7051052]$ |
\(y^2=x^3-69312x-7051052\) |
38.2.0.a.1 |
$[ ]$ |
| 12996.j1 |
12996j1 |
12996.j |
12996j |
$1$ |
$1$ |
\( 2^{2} \cdot 3^{2} \cdot 19^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 19^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 5$ |
2.2.0.1, 5.5.0.1 |
2Cn, 5S4 |
$1140$ |
$60$ |
$2$ |
$4.305924817$ |
$1$ |
|
$2$ |
$30780$ |
$1.458672$ |
$4864$ |
$0.64811$ |
$4.37159$ |
$[0, 0, 0, -20577, -912247]$ |
\(y^2=x^3-20577x-912247\) |
2.2.0.a.1, 5.5.0.a.1, 10.10.0.a.1, 12.4.0-2.a.1.1, 38.6.0.a.1, $\ldots$ |
$[(-67, 407)]$ |
| 12996.k1 |
12996m1 |
12996.k |
12996m |
$1$ |
$1$ |
\( 2^{2} \cdot 3^{2} \cdot 19^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 19^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 5$ |
2.2.0.1, 5.5.0.1 |
2Cn, 5S4 |
$1140$ |
$60$ |
$2$ |
$1$ |
$1$ |
|
$0$ |
$1620$ |
$-0.013548$ |
$4864$ |
$0.64811$ |
$2.50652$ |
$[0, 0, 0, -57, 133]$ |
\(y^2=x^3-57x+133\) |
2.2.0.a.1, 5.5.0.a.1, 10.10.0.a.1, 38.6.0.a.1, 190.30.2.?, $\ldots$ |
$[ ]$ |
| 12996.l1 |
12996l1 |
12996.l |
12996l |
$1$ |
$1$ |
\( 2^{2} \cdot 3^{2} \cdot 19^{2} \) |
\( - 2^{8} \cdot 3^{10} \cdot 19^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.4.0.1 |
|
$76$ |
$8$ |
$0$ |
$1.327575377$ |
$1$ |
|
$2$ |
$7680$ |
$0.807219$ |
$-65536/81$ |
$1.10590$ |
$3.50528$ |
$[0, 0, 0, -912, 18772]$ |
\(y^2=x^3-912x+18772\) |
4.4.0.a.1, 38.2.0.a.1, 76.8.0.? |
$[(-19, 171)]$ |
| 12996.m1 |
12996k1 |
12996.m |
12996k |
$1$ |
$1$ |
\( 2^{2} \cdot 3^{2} \cdot 19^{2} \) |
\( - 2^{8} \cdot 3^{10} \cdot 19^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.4.0.1 |
|
$76$ |
$8$ |
$0$ |
$4.744426944$ |
$1$ |
|
$0$ |
$145920$ |
$2.279438$ |
$-65536/81$ |
$1.10590$ |
$5.37034$ |
$[0, 0, 0, -329232, -128757148]$ |
\(y^2=x^3-329232x-128757148\) |
4.4.0.a.1, 38.2.0.a.1, 76.8.0.? |
$[(53428/7, 9753498/7)]$ |
| 12996.n1 |
12996p1 |
12996.n |
12996p |
$1$ |
$1$ |
\( 2^{2} \cdot 3^{2} \cdot 19^{2} \) |
\( - 2^{8} \cdot 3^{8} \cdot 19^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$38$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$69120$ |
$1.592421$ |
$8192/171$ |
$0.94370$ |
$4.47318$ |
$[0, 0, 0, 8664, 1838212]$ |
\(y^2=x^3+8664x+1838212\) |
38.2.0.a.1 |
$[ ]$ |
| 12996.o1 |
12996h1 |
12996.o |
12996h |
$1$ |
$1$ |
\( 2^{2} \cdot 3^{2} \cdot 19^{2} \) |
\( - 2^{4} \cdot 3^{3} \cdot 19^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 5$ |
4.4.0.1, 5.5.0.1 |
5S4 |
$60$ |
$40$ |
$2$ |
$7.353497057$ |
$1$ |
|
$0$ |
$6912$ |
$0.324324$ |
$-1815478272$ |
$1.37833$ |
$3.51304$ |
$[0, 0, 0, -1368, -19475]$ |
\(y^2=x^3-1368x-19475\) |
4.4.0.a.1, 5.5.0.a.1, 6.2.0.a.1, 12.8.0.c.1, 20.20.1.c.1, $\ldots$ |
$[(2171/5, 89844/5)]$ |
| 12996.p1 |
12996c1 |
12996.p |
12996c |
$1$ |
$1$ |
\( 2^{2} \cdot 3^{2} \cdot 19^{2} \) |
\( - 2^{4} \cdot 3^{3} \cdot 19^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 5$ |
4.4.0.1, 5.5.0.1 |
5S4 |
$60$ |
$40$ |
$2$ |
$1$ |
$1$ |
|
$0$ |
$131328$ |
$1.796543$ |
$-1815478272$ |
$1.37833$ |
$5.37811$ |
$[0, 0, 0, -493848, 133579025]$ |
\(y^2=x^3-493848x+133579025\) |
4.4.0.a.1, 5.5.0.a.1, 6.2.0.a.1, 12.8.0.c.1, 20.20.1.c.1, $\ldots$ |
$[ ]$ |
