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 |
171.a1 |
171a3 |
171.a |
171a |
$4$ |
$4$ |
\( 3^{2} \cdot 19 \) |
\( 3^{10} \cdot 19 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.6 |
2B |
$456$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$48$ |
$0.304297$ |
$115714886617/1539$ |
$0.98111$ |
$6.23652$ |
$[1, -1, 1, -914, -10402]$ |
\(y^2+xy+y=x^3-x^2-914x-10402\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.2, 24.24.0-24.z.1.4, $\ldots$ |
$[]$ |
171.a2 |
171a2 |
171.a |
171a |
$4$ |
$4$ |
\( 3^{2} \cdot 19 \) |
\( 3^{8} \cdot 19^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.1 |
2Cs |
$228$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$24$ |
$-0.042276$ |
$30664297/3249$ |
$0.90727$ |
$4.63474$ |
$[1, -1, 1, -59, -142]$ |
\(y^2+xy+y=x^3-x^2-59x-142\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.b.1.2, 76.24.0.?, 228.48.0.? |
$[]$ |
171.a3 |
171a1 |
171.a |
171a |
$4$ |
$4$ |
\( 3^{2} \cdot 19 \) |
\( 3^{7} \cdot 19 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.7 |
2B |
$456$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$12$ |
$-0.388850$ |
$389017/57$ |
$0.96267$ |
$3.78536$ |
$[1, -1, 1, -14, 20]$ |
\(y^2+xy+y=x^3-x^2-14x+20\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.z.1.8, 114.6.0.?, 152.24.0.?, $\ldots$ |
$[]$ |
171.a4 |
171a4 |
171.a |
171a |
$4$ |
$4$ |
\( 3^{2} \cdot 19 \) |
\( - 3^{7} \cdot 19^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.8 |
2B |
$456$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$48$ |
$0.304297$ |
$67419143/390963$ |
$0.97474$ |
$5.21575$ |
$[1, -1, 1, 76, -790]$ |
\(y^2+xy+y=x^3-x^2+76x-790\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 6.6.0.a.1, 12.24.0-12.g.1.1, 152.24.0.?, $\ldots$ |
$[]$ |
171.b1 |
171b3 |
171.b |
171b |
$3$ |
$9$ |
\( 3^{2} \cdot 19 \) |
\( - 3^{6} \cdot 19 \) |
$1$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
27.72.0.1 |
3B.1.1 |
$1026$ |
$1296$ |
$43$ |
$2.033701819$ |
$1$ |
|
$4$ |
$72$ |
$0.582746$ |
$-50357871050752/19$ |
$1.10495$ |
$7.41819$ |
$[0, 0, 1, -6924, 221760]$ |
\(y^2+y=x^3-6924x+221760\) |
3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 27.72.0-27.a.1.2, 38.2.0.a.1, 114.16.0.?, $\ldots$ |
$[(62, 175)]$ |
171.b2 |
171b2 |
171.b |
171b |
$3$ |
$9$ |
\( 3^{2} \cdot 19 \) |
\( - 3^{6} \cdot 19^{3} \) |
$1$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.72.0.3 |
3Cs.1.1 |
$1026$ |
$1296$ |
$43$ |
$0.677900606$ |
$1$ |
|
$8$ |
$24$ |
$0.033439$ |
$-89915392/6859$ |
$1.03310$ |
$4.86805$ |
$[0, 0, 1, -84, 315]$ |
\(y^2+y=x^3-84x+315\) |
3.24.0-3.a.1.1, 9.72.0-9.b.1.1, 38.2.0.a.1, 114.48.1.?, 171.216.4.?, $\ldots$ |
$[(5, 4)]$ |
171.b3 |
171b1 |
171.b |
171b |
$3$ |
$9$ |
\( 3^{2} \cdot 19 \) |
\( - 3^{6} \cdot 19 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
27.72.0.2 |
3B.1.2 |
$1026$ |
$1296$ |
$43$ |
$0.225966868$ |
$1$ |
|
$6$ |
$8$ |
$-0.515867$ |
$32768/19$ |
$1.31757$ |
$3.30416$ |
$[0, 0, 1, 6, 0]$ |
\(y^2+y=x^3+6x\) |
3.8.0-3.a.1.1, 9.24.0-9.a.1.1, 27.72.0-27.a.1.1, 38.2.0.a.1, 114.16.0.?, $\ldots$ |
$[(2, 4)]$ |
171.c1 |
171c2 |
171.c |
171c |
$2$ |
$5$ |
\( 3^{2} \cdot 19 \) |
\( - 3^{8} \cdot 19^{5} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.12.0.2 |
5B.4.2 |
$570$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$480$ |
$1.200714$ |
$-9358714467168256/22284891$ |
$1.06833$ |
$8.43438$ |
$[0, 0, 1, -39513, 3023145]$ |
\(y^2+y=x^3-39513x+3023145\) |
5.12.0.a.2, 15.24.0-5.a.2.1, 38.2.0.a.1, 190.24.1.?, 570.48.1.? |
$[]$ |
171.c2 |
171c1 |
171.c |
171c |
$2$ |
$5$ |
\( 3^{2} \cdot 19 \) |
\( - 3^{16} \cdot 19 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.12.0.1 |
5B.4.1 |
$570$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$96$ |
$0.395995$ |
$841232384/1121931$ |
$1.00490$ |
$5.33056$ |
$[0, 0, 1, 177, 1035]$ |
\(y^2+y=x^3+177x+1035\) |
5.12.0.a.1, 15.24.0-5.a.1.1, 38.2.0.a.1, 190.24.1.?, 570.48.1.? |
$[]$ |
171.d1 |
171d1 |
171.d |
171d |
$1$ |
$1$ |
\( 3^{2} \cdot 19 \) |
\( - 3^{8} \cdot 19 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$38$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$32$ |
$-0.287242$ |
$-1404928/171$ |
$0.86512$ |
$4.07223$ |
$[0, 0, 1, -21, -41]$ |
\(y^2+y=x^3-21x-41\) |
38.2.0.a.1 |
$[]$ |