| 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 |
Intrinsic torsion order |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
Manin constant |
| 1216.a1 |
1216r1 |
1216.a |
1216r |
$1$ |
$1$ |
\( 2^{6} \cdot 19 \) |
\( - 2^{15} \cdot 19 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$152$ |
$2$ |
$0$ |
$0.225942131$ |
$1$ |
|
$6$ |
$192$ |
$-0.199705$ |
$27000/19$ |
$0.79171$ |
$2.90016$ |
|
$[0, 0, 0, 20, 16]$ |
\(y^2=x^3+20x+16\) |
152.2.0.? |
$[(2, 8)]$ |
$1$ |
| 1216.b1 |
1216q3 |
1216.b |
1216q |
$3$ |
$9$ |
\( 2^{6} \cdot 19 \) |
\( - 2^{6} \cdot 19 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
27.36.0.1 |
3B |
$4104$ |
$1296$ |
$43$ |
$0.595904332$ |
$1$ |
|
$2$ |
$432$ |
$0.380013$ |
$-50357871050752/19$ |
$1.10495$ |
$5.02709$ |
|
$[0, 1, 0, -3077, 64681]$ |
\(y^2=x^3+x^2-3077x+64681\) |
3.4.0.a.1, 9.12.0.a.1, 24.8.0-3.a.1.3, 27.36.0.a.1, 38.2.0.a.1, $\ldots$ |
$[(32, 3)]$ |
$1$ |
| 1216.b2 |
1216q2 |
1216.b |
1216q |
$3$ |
$9$ |
\( 2^{6} \cdot 19 \) |
\( - 2^{6} \cdot 19^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.36.0.2 |
3Cs |
$4104$ |
$1296$ |
$43$ |
$0.198634777$ |
$1$ |
|
$4$ |
$144$ |
$-0.169293$ |
$-89915392/6859$ |
$1.03310$ |
$3.18120$ |
|
$[0, 1, 0, -37, 81]$ |
\(y^2=x^3+x^2-37x+81\) |
3.12.0.a.1, 9.36.0.b.1, 24.24.0-3.a.1.2, 38.2.0.a.1, 72.72.0.?, $\ldots$ |
$[(8, 19)]$ |
$1$ |
| 1216.b3 |
1216q1 |
1216.b |
1216q |
$3$ |
$9$ |
\( 2^{6} \cdot 19 \) |
\( - 2^{6} \cdot 19 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
27.36.0.1 |
3B |
$4104$ |
$1296$ |
$43$ |
$0.595904332$ |
$1$ |
|
$2$ |
$48$ |
$-0.718599$ |
$32768/19$ |
$1.31757$ |
$2.04919$ |
|
$[0, 1, 0, 3, 1]$ |
\(y^2=x^3+x^2+3x+1\) |
3.4.0.a.1, 9.12.0.a.1, 24.8.0-3.a.1.4, 27.36.0.a.1, 38.2.0.a.1, $\ldots$ |
$[(0, 1)]$ |
$1$ |
| 1216.c1 |
1216h1 |
1216.c |
1216h |
$1$ |
$1$ |
\( 2^{6} \cdot 19 \) |
\( - 2^{14} \cdot 19 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$38$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$192$ |
$-0.094357$ |
$-4194304/19$ |
$1.07903$ |
$3.51400$ |
|
$[0, 1, 0, -85, -333]$ |
\(y^2=x^3+x^2-85x-333\) |
38.2.0.a.1 |
$[ ]$ |
$1$ |
| 1216.d1 |
1216l1 |
1216.d |
1216l |
$1$ |
$1$ |
\( 2^{6} \cdot 19 \) |
\( - 2^{14} \cdot 19 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$38$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$128$ |
$-0.264905$ |
$-1024/19$ |
$0.79665$ |
$2.83444$ |
|
$[0, 1, 0, -5, -29]$ |
\(y^2=x^3+x^2-5x-29\) |
38.2.0.a.1 |
$[ ]$ |
$1$ |
| 1216.e1 |
1216b3 |
1216.e |
1216b |
$3$ |
$9$ |
\( 2^{6} \cdot 19 \) |
\( - 2^{45} \cdot 19 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
27.36.0.1 |
3B |
$4104$ |
$1296$ |
$43$ |
$2.504328284$ |
$1$ |
|
$0$ |
$3456$ |
$1.524891$ |
$-69173457625/2550136832$ |
$1.05462$ |
$5.85731$ |
|
$[0, -1, 0, -5473, -1251871]$ |
\(y^2=x^3-x^2-5473x-1251871\) |
3.4.0.a.1, 9.12.0.a.1, 24.8.0-3.a.1.1, 27.36.0.a.1, 72.24.0.?, $\ldots$ |
$[(6745/7, 262144/7)]$ |
$1$ |
| 1216.e2 |
1216b1 |
1216.e |
1216b |
$3$ |
$9$ |
\( 2^{6} \cdot 19 \) |
\( - 2^{21} \cdot 19 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
27.36.0.1 |
3B |
$4104$ |
$1296$ |
$43$ |
$0.278258698$ |
$1$ |
|
$4$ |
$384$ |
$0.426278$ |
$-413493625/152$ |
$0.93281$ |
$4.54962$ |
|
$[0, -1, 0, -993, 12385]$ |
\(y^2=x^3-x^2-993x+12385\) |
3.4.0.a.1, 9.12.0.a.1, 24.8.0-3.a.1.2, 27.36.0.a.1, 72.24.0.?, $\ldots$ |
$[(9, 64)]$ |
$1$ |
| 1216.e3 |
1216b2 |
1216.e |
1216b |
$3$ |
$9$ |
\( 2^{6} \cdot 19 \) |
\( - 2^{27} \cdot 19^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.36.0.2 |
3Cs |
$4104$ |
$1296$ |
$43$ |
$0.834776094$ |
$1$ |
|
$4$ |
$1152$ |
$0.975584$ |
$94196375/3511808$ |
$1.01875$ |
$4.92549$ |
|
$[0, -1, 0, 607, 45601]$ |
\(y^2=x^3-x^2+607x+45601\) |
3.12.0.a.1, 9.36.0.b.1, 24.24.0-3.a.1.1, 72.72.0.?, 114.24.0.?, $\ldots$ |
$[(57, 512)]$ |
$1$ |
| 1216.f1 |
1216c1 |
1216.f |
1216c |
$1$ |
$1$ |
\( 2^{6} \cdot 19 \) |
\( - 2^{17} \cdot 19 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$152$ |
$2$ |
$0$ |
$0.602396728$ |
$1$ |
|
$4$ |
$128$ |
$-0.070605$ |
$-31250/19$ |
$0.89957$ |
$3.21700$ |
|
$[0, -1, 0, -33, -95]$ |
\(y^2=x^3-x^2-33x-95\) |
152.2.0.? |
$[(9, 16)]$ |
$1$ |
| 1216.g1 |
1216j2 |
1216.g |
1216j |
$2$ |
$5$ |
\( 2^{6} \cdot 19 \) |
\( - 2^{19} \cdot 19^{5} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.12.0.2 |
5B.4.2 |
$760$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$1920$ |
$1.057505$ |
$-37966934881/4952198$ |
$0.97714$ |
$5.21445$ |
|
$[0, -1, 0, -4481, 129313]$ |
\(y^2=x^3-x^2-4481x+129313\) |
5.12.0.a.2, 40.24.0-5.a.2.1, 152.2.0.?, 380.24.0.?, 760.48.1.? |
$[ ]$ |
$1$ |
| 1216.g2 |
1216j1 |
1216.g |
1216j |
$2$ |
$5$ |
\( 2^{6} \cdot 19 \) |
\( - 2^{23} \cdot 19 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.12.0.1 |
5B.4.1 |
$760$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$384$ |
$0.252787$ |
$-1/608$ |
$1.37833$ |
$3.70834$ |
|
$[0, -1, 0, -1, -607]$ |
\(y^2=x^3-x^2-x-607\) |
5.12.0.a.1, 40.24.0-5.a.1.1, 152.2.0.?, 380.24.0.?, 760.48.1.? |
$[ ]$ |
$1$ |
| 1216.h1 |
1216i1 |
1216.h |
1216i |
$1$ |
$1$ |
\( 2^{6} \cdot 19 \) |
\( - 2^{6} \cdot 19^{5} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.15.0.1 |
5Ns |
$380$ |
$60$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$480$ |
$0.252518$ |
$-4741632/2476099$ |
$1.30327$ |
$3.70769$ |
|
$[0, 0, 0, -14, -606]$ |
\(y^2=x^3-14x-606\) |
5.15.0.a.1, 20.30.0.a.1, 38.2.0.a.1, 190.30.2.?, 380.60.3.? |
$[ ]$ |
$1$ |
| 1216.i1 |
1216n1 |
1216.i |
1216n |
$1$ |
$1$ |
\( 2^{6} \cdot 19 \) |
\( - 2^{6} \cdot 19^{5} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.15.0.1 |
5Ns |
$380$ |
$60$ |
$3$ |
$0.328891621$ |
$1$ |
|
$2$ |
$480$ |
$0.252518$ |
$-4741632/2476099$ |
$1.30327$ |
$3.70769$ |
|
$[0, 0, 0, -14, 606]$ |
\(y^2=x^3-14x+606\) |
5.15.0.a.1, 20.30.0.a.1, 38.2.0.a.1, 190.30.2.?, 380.60.3.? |
$[(-7, 19)]$ |
$1$ |
| 1216.j1 |
1216a1 |
1216.j |
1216a |
$1$ |
$1$ |
\( 2^{6} \cdot 19 \) |
\( - 2^{6} \cdot 19 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$38$ |
$2$ |
$0$ |
$0.595835310$ |
$1$ |
|
$2$ |
$32$ |
$-0.715568$ |
$-13824/19$ |
$0.69588$ |
$2.09894$ |
|
$[0, 0, 0, -2, 2]$ |
\(y^2=x^3-2x+2\) |
38.2.0.a.1 |
$[(1, 1)]$ |
$1$ |
| 1216.k1 |
1216e1 |
1216.k |
1216e |
$1$ |
$1$ |
\( 2^{6} \cdot 19 \) |
\( - 2^{6} \cdot 19 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$38$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$32$ |
$-0.715568$ |
$-13824/19$ |
$0.69588$ |
$2.09894$ |
|
$[0, 0, 0, -2, -2]$ |
\(y^2=x^3-2x-2\) |
38.2.0.a.1 |
$[ ]$ |
$1$ |
| 1216.l1 |
1216p1 |
1216.l |
1216p |
$1$ |
$1$ |
\( 2^{6} \cdot 19 \) |
\( - 2^{17} \cdot 19 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$152$ |
$2$ |
$0$ |
$0.294246876$ |
$1$ |
|
$4$ |
$128$ |
$-0.070605$ |
$-31250/19$ |
$0.89957$ |
$3.21700$ |
|
$[0, 1, 0, -33, 95]$ |
\(y^2=x^3+x^2-33x+95\) |
152.2.0.? |
$[(7, 16)]$ |
$1$ |
| 1216.m1 |
1216o3 |
1216.m |
1216o |
$3$ |
$9$ |
\( 2^{6} \cdot 19 \) |
\( - 2^{45} \cdot 19 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
27.36.0.1 |
3B |
$4104$ |
$1296$ |
$43$ |
$1.698405069$ |
$1$ |
|
$0$ |
$3456$ |
$1.524891$ |
$-69173457625/2550136832$ |
$1.05462$ |
$5.85731$ |
|
$[0, 1, 0, -5473, 1251871]$ |
\(y^2=x^3+x^2-5473x+1251871\) |
3.4.0.a.1, 9.12.0.a.1, 24.8.0-3.a.1.3, 27.36.0.a.1, 72.24.0.?, $\ldots$ |
$[(4111/3, 262144/3)]$ |
$1$ |
| 1216.m2 |
1216o1 |
1216.m |
1216o |
$3$ |
$9$ |
\( 2^{6} \cdot 19 \) |
\( - 2^{21} \cdot 19 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
27.36.0.1 |
3B |
$4104$ |
$1296$ |
$43$ |
$1.698405069$ |
$1$ |
|
$2$ |
$384$ |
$0.426278$ |
$-413493625/152$ |
$0.93281$ |
$4.54962$ |
|
$[0, 1, 0, -993, -12385]$ |
\(y^2=x^3+x^2-993x-12385\) |
3.4.0.a.1, 9.12.0.a.1, 24.8.0-3.a.1.4, 27.36.0.a.1, 72.24.0.?, $\ldots$ |
$[(55, 320)]$ |
$1$ |
| 1216.m3 |
1216o2 |
1216.m |
1216o |
$3$ |
$9$ |
\( 2^{6} \cdot 19 \) |
\( - 2^{27} \cdot 19^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.36.0.2 |
3Cs |
$4104$ |
$1296$ |
$43$ |
$0.566135023$ |
$1$ |
|
$4$ |
$1152$ |
$0.975584$ |
$94196375/3511808$ |
$1.01875$ |
$4.92549$ |
|
$[0, 1, 0, 607, -45601]$ |
\(y^2=x^3+x^2+607x-45601\) |
3.12.0.a.1, 9.36.0.b.1, 24.24.0-3.a.1.2, 72.72.0.?, 152.2.0.?, $\ldots$ |
$[(455, 9728)]$ |
$1$ |
| 1216.n1 |
1216f2 |
1216.n |
1216f |
$2$ |
$5$ |
\( 2^{6} \cdot 19 \) |
\( - 2^{19} \cdot 19^{5} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.12.0.2 |
5B.4.2 |
$760$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$1920$ |
$1.057505$ |
$-37966934881/4952198$ |
$0.97714$ |
$5.21445$ |
|
$[0, 1, 0, -4481, -129313]$ |
\(y^2=x^3+x^2-4481x-129313\) |
5.12.0.a.2, 40.24.0-5.a.2.3, 152.2.0.?, 190.24.0.?, 760.48.1.? |
$[ ]$ |
$1$ |
| 1216.n2 |
1216f1 |
1216.n |
1216f |
$2$ |
$5$ |
\( 2^{6} \cdot 19 \) |
\( - 2^{23} \cdot 19 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.12.0.1 |
5B.4.1 |
$760$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$384$ |
$0.252787$ |
$-1/608$ |
$1.37833$ |
$3.70834$ |
|
$[0, 1, 0, -1, 607]$ |
\(y^2=x^3+x^2-x+607\) |
5.12.0.a.1, 40.24.0-5.a.1.3, 152.2.0.?, 190.24.0.?, 760.48.1.? |
$[ ]$ |
$1$ |
| 1216.o1 |
1216d3 |
1216.o |
1216d |
$3$ |
$9$ |
\( 2^{6} \cdot 19 \) |
\( - 2^{6} \cdot 19 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
27.36.0.1 |
3B |
$4104$ |
$1296$ |
$43$ |
$9.167331319$ |
$1$ |
|
$0$ |
$432$ |
$0.380013$ |
$-50357871050752/19$ |
$1.10495$ |
$5.02709$ |
|
$[0, -1, 0, -3077, -64681]$ |
\(y^2=x^3-x^2-3077x-64681\) |
3.4.0.a.1, 9.12.0.a.1, 24.8.0-3.a.1.1, 27.36.0.a.1, 38.2.0.a.1, $\ldots$ |
$[(8026/7, 668541/7)]$ |
$1$ |
| 1216.o2 |
1216d2 |
1216.o |
1216d |
$3$ |
$9$ |
\( 2^{6} \cdot 19 \) |
\( - 2^{6} \cdot 19^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.36.0.2 |
3Cs |
$4104$ |
$1296$ |
$43$ |
$3.055777106$ |
$1$ |
|
$2$ |
$144$ |
$-0.169293$ |
$-89915392/6859$ |
$1.03310$ |
$3.18120$ |
|
$[0, -1, 0, -37, -81]$ |
\(y^2=x^3-x^2-37x-81\) |
3.12.0.a.1, 9.36.0.b.1, 24.24.0-3.a.1.1, 38.2.0.a.1, 72.72.0.?, $\ldots$ |
$[(18, 69)]$ |
$1$ |
| 1216.o3 |
1216d1 |
1216.o |
1216d |
$3$ |
$9$ |
\( 2^{6} \cdot 19 \) |
\( - 2^{6} \cdot 19 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
27.36.0.1 |
3B |
$4104$ |
$1296$ |
$43$ |
$1.018592368$ |
$1$ |
|
$2$ |
$48$ |
$-0.718599$ |
$32768/19$ |
$1.31757$ |
$2.04919$ |
|
$[0, -1, 0, 3, -1]$ |
\(y^2=x^3-x^2+3x-1\) |
3.4.0.a.1, 9.12.0.a.1, 24.8.0-3.a.1.2, 27.36.0.a.1, 38.2.0.a.1, $\ldots$ |
$[(2, 3)]$ |
$1$ |
| 1216.p1 |
1216g1 |
1216.p |
1216g |
$1$ |
$1$ |
\( 2^{6} \cdot 19 \) |
\( - 2^{14} \cdot 19 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$38$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$128$ |
$-0.264905$ |
$-1024/19$ |
$0.79665$ |
$2.83444$ |
|
$[0, -1, 0, -5, 29]$ |
\(y^2=x^3-x^2-5x+29\) |
38.2.0.a.1 |
$[ ]$ |
$1$ |
| 1216.q1 |
1216k1 |
1216.q |
1216k |
$1$ |
$1$ |
\( 2^{6} \cdot 19 \) |
\( - 2^{14} \cdot 19 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$38$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$192$ |
$-0.094357$ |
$-4194304/19$ |
$1.07903$ |
$3.51400$ |
|
$[0, -1, 0, -85, 333]$ |
\(y^2=x^3-x^2-85x+333\) |
38.2.0.a.1 |
$[ ]$ |
$1$ |
| 1216.r1 |
1216m1 |
1216.r |
1216m |
$1$ |
$1$ |
\( 2^{6} \cdot 19 \) |
\( - 2^{15} \cdot 19 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$152$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$192$ |
$-0.199705$ |
$27000/19$ |
$0.79171$ |
$2.90016$ |
|
$[0, 0, 0, 20, -16]$ |
\(y^2=x^3+20x-16\) |
152.2.0.? |
$[ ]$ |
$1$ |
