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 |
Regulator |
$Ш_{\textrm{an}}$ |
Ш primes |
Integral points |
Modular degree |
Faltings height |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
114.a1 |
114b1 |
114.a |
114b |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 19 \) |
\( 2^{2} \cdot 3^{5} \cdot 19 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.4 |
2B |
$1$ |
$1$ |
|
$1$ |
$20$ |
$-0.180691$ |
$96386901625/18468$ |
$[1, 1, 0, -95, -399]$ |
\(y^2+xy=x^3+x^2-95x-399\) |
114.a2 |
114b2 |
114.a |
114b |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 19 \) |
\( - 2 \cdot 3^{10} \cdot 19^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.5 |
2B |
$1$ |
$1$ |
|
$0$ |
$40$ |
$0.165883$ |
$-69173457625/42633378$ |
$[1, 1, 0, -85, -473]$ |
\(y^2+xy=x^3+x^2-85x-473\) |
114.b1 |
114c3 |
114.b |
114c |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 19 \) |
\( 2^{5} \cdot 3^{3} \cdot 19 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.102 |
2B |
$1$ |
$4$ |
$2$ |
$0$ |
$240$ |
$1.101439$ |
$74220219816682217473/16416$ |
$[1, 1, 1, -87552, -10007679]$ |
\(y^2+xy+y=x^3+x^2-87552x-10007679\) |
114.b2 |
114c2 |
114.b |
114c |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 19 \) |
\( 2^{10} \cdot 3^{6} \cdot 19^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.4 |
2Cs |
$1$ |
$1$ |
|
$2$ |
$120$ |
$0.754866$ |
$18120364883707393/269485056$ |
$[1, 1, 1, -5472, -158079]$ |
\(y^2+xy+y=x^3+x^2-5472x-158079\) |
114.b3 |
114c4 |
114.b |
114c |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 19 \) |
\( - 2^{5} \cdot 3^{12} \cdot 19^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.59 |
2B |
$1$ |
$1$ |
|
$0$ |
$240$ |
$1.101439$ |
$-16576888679672833/2216253521952$ |
$[1, 1, 1, -5312, -167551]$ |
\(y^2+xy+y=x^3+x^2-5312x-167551\) |
114.b4 |
114c1 |
114.b |
114c |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 19 \) |
\( 2^{20} \cdot 3^{3} \cdot 19 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.53 |
2B |
$1$ |
$1$ |
|
$3$ |
$60$ |
$0.408292$ |
$4824238966273/537919488$ |
$[1, 1, 1, -352, -2431]$ |
\(y^2+xy+y=x^3+x^2-352x-2431\) |
114.c1 |
114a3 |
114.c |
114a |
$4$ |
$6$ |
\( 2 \cdot 3 \cdot 19 \) |
\( 2^{2} \cdot 3 \cdot 19^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
8.6.0.4, 3.8.0.2 |
2B, 3B.1.2 |
$1$ |
$1$ |
|
$1$ |
$36$ |
$0.105502$ |
$8671983378625/82308$ |
$[1, 0, 0, -428, -3444]$ |
\(y^2+xy=x^3-428x-3444\) |
114.c2 |
114a4 |
114.c |
114a |
$4$ |
$6$ |
\( 2 \cdot 3 \cdot 19 \) |
\( - 2 \cdot 3^{2} \cdot 19^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
8.6.0.5, 3.8.0.2 |
2B, 3B.1.2 |
$1$ |
$1$ |
|
$0$ |
$72$ |
$0.452075$ |
$-8078253774625/846825858$ |
$[1, 0, 0, -418, -3610]$ |
\(y^2+xy=x^3-418x-3610\) |
114.c3 |
114a1 |
114.c |
114a |
$4$ |
$6$ |
\( 2 \cdot 3 \cdot 19 \) |
\( 2^{6} \cdot 3^{3} \cdot 19 \) |
$0$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
8.6.0.4, 3.8.0.1 |
2B, 3B.1.1 |
$1$ |
$1$ |
|
$5$ |
$12$ |
$-0.443804$ |
$57066625/32832$ |
$[1, 0, 0, -8, 0]$ |
\(y^2+xy=x^3-8x\) |
114.c4 |
114a2 |
114.c |
114a |
$4$ |
$6$ |
\( 2 \cdot 3 \cdot 19 \) |
\( - 2^{3} \cdot 3^{6} \cdot 19^{2} \) |
$0$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
8.6.0.5, 3.8.0.1 |
2B, 3B.1.1 |
$1$ |
$1$ |
|
$4$ |
$24$ |
$-0.097231$ |
$3616805375/2105352$ |
$[1, 0, 0, 32, 8]$ |
\(y^2+xy=x^3+32x+8\) |