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 |
31939.a1 |
31939c1 |
31939.a |
31939c |
$1$ |
$1$ |
\( 19 \cdot 41^{2} \) |
\( - 19 \cdot 41^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$38$ |
$2$ |
$0$ |
$1.080892177$ |
$1$ |
|
$4$ |
$3360$ |
$-0.449940$ |
$14063/19$ |
$[1, 0, 0, 6, 7]$ |
\(y^2+xy=x^3+6x+7\) |
38.2.0.a.1 |
$[(-1, 1)]$ |
31939.b1 |
31939e1 |
31939.b |
31939e |
$1$ |
$1$ |
\( 19 \cdot 41^{2} \) |
\( - 19 \cdot 41^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$38$ |
$2$ |
$0$ |
$5.879925883$ |
$1$ |
|
$0$ |
$137760$ |
$1.406845$ |
$14063/19$ |
$[1, 1, 1, 10051, 452254]$ |
\(y^2+xy+y=x^3+x^2+10051x+452254\) |
38.2.0.a.1 |
$[(33106/15, 7404451/15)]$ |
31939.c1 |
31939d1 |
31939.c |
31939d |
$1$ |
$1$ |
\( 19 \cdot 41^{2} \) |
\( - 19 \cdot 41^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$1558$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$2800$ |
$-0.123475$ |
$-32768/19$ |
$[0, -1, 1, -27, -69]$ |
\(y^2+y=x^3-x^2-27x-69\) |
1558.2.0.? |
$[]$ |
31939.d1 |
31939a1 |
31939.d |
31939a |
$1$ |
$1$ |
\( 19 \cdot 41^{2} \) |
\( - 19 \cdot 41^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$1558$ |
$2$ |
$0$ |
$15.86433597$ |
$1$ |
|
$0$ |
$114800$ |
$1.733311$ |
$-32768/19$ |
$[0, 1, 1, -45947, -5379029]$ |
\(y^2+y=x^3+x^2-45947x-5379029\) |
1558.2.0.? |
$[(1998764167/537, 89322737970626/537)]$ |
31939.e1 |
31939b3 |
31939.e |
31939b |
$3$ |
$9$ |
\( 19 \cdot 41^{2} \) |
\( - 19 \cdot 41^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
27.36.0.1 |
3B |
$42066$ |
$1296$ |
$43$ |
$60.32974189$ |
$1$ |
|
$0$ |
$207360$ |
$1.890224$ |
$-50357871050752/19$ |
$[0, -1, 1, -1293249, -565640702]$ |
\(y^2+y=x^3-x^2-1293249x-565640702\) |
3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 38.2.0.a.1, 114.8.0.?, $\ldots$ |
$[(4490897913973861300437037109/1754579504530, 137706327894684946735684190677072440042127/1754579504530)]$ |
31939.e2 |
31939b2 |
31939.e |
31939b |
$3$ |
$9$ |
\( 19 \cdot 41^{2} \) |
\( - 19^{3} \cdot 41^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.36.0.2 |
3Cs |
$42066$ |
$1296$ |
$43$ |
$20.10991396$ |
$1$ |
|
$0$ |
$69120$ |
$1.340919$ |
$-89915392/6859$ |
$[0, -1, 1, -15689, -799487]$ |
\(y^2+y=x^3-x^2-15689x-799487\) |
3.12.0.a.1, 9.36.0.b.1, 38.2.0.a.1, 114.24.1.?, 123.24.0.?, $\ldots$ |
$[(14859337909/10030, 291658245296977/10030)]$ |
31939.e3 |
31939b1 |
31939.e |
31939b |
$3$ |
$9$ |
\( 19 \cdot 41^{2} \) |
\( - 19 \cdot 41^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
27.36.0.1 |
3B |
$42066$ |
$1296$ |
$43$ |
$6.703304654$ |
$1$ |
|
$0$ |
$23040$ |
$0.791613$ |
$32768/19$ |
$[0, -1, 1, 1121, -1012]$ |
\(y^2+y=x^3-x^2+1121x-1012\) |
3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 38.2.0.a.1, 114.8.0.?, $\ldots$ |
$[(28236/17, 4987592/17)]$ |