Label |
Class |
Conductor |
Discriminant |
Rank* |
2-Selmer rank |
Torsion |
$\textrm{End}^0(J_{\overline\Q})$ |
$\textrm{End}^0(J)$ |
$\GL_2\textsf{-type}$ |
Sato-Tate |
Nonmaximal primes |
$\Q$-simple |
\(\overline{\Q}\)-simple |
\(\Aut(X)\) |
\(\Aut(X_{\overline{\Q}})\) |
$\Q$-points |
$\Q$-Weierstrass points |
mod-$\ell$ images |
Locally solvable |
Square Ш* |
Analytic Ш* |
Tamagawa |
Regulator |
Real period |
Leading coefficient |
Igusa-Clebsch invariants |
Igusa invariants |
G2-invariants |
Equation |
847.a.847.1 |
847.a |
\( 7 \cdot 11^{2} \) |
\( - 7 \cdot 11^{2} \) |
$1$ |
$1$ |
$\Z/5\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.15.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.196056\) |
\(20.305961\) |
\(0.159244\) |
$[120,276,6864,3388]$ |
$[60,104,504,4856,847]$ |
$[777600000/847,22464000/847,259200/121]$ |
$y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^3 + x^2$ |
847.b.9317.1 |
847.b |
\( 7 \cdot 11^{2} \) |
\( 7 \cdot 11^{3} \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1, 3.80.4 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(16.827271\) |
\(0.336545\) |
$[304,5932,452465,-37268]$ |
$[152,-26,-401,-15407,-9317]$ |
$[-81136812032/9317,91307008/9317,9264704/9317]$ |
$y^2 + (x^2 + 1)y = x^5 + 2x^4 - 3x^3 + 2x^2 - x$ |
847.c.9317.1 |
847.c |
\( 7 \cdot 11^{2} \) |
\( 7 \cdot 11^{3} \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(9.983400\) |
\(0.311981\) |
$[424,3520,581427,37268]$ |
$[212,1286,-7999,-837396,9317]$ |
$[428232184832/9317,12253172608/9317,-359507056/9317]$ |
$y^2 + (x^3 + x^2)y = x^4 + x^3 - x - 2$ |
847.d.847.1 |
847.d |
\( 7 \cdot 11^{2} \) |
\( - 7 \cdot 11^{2} \) |
$0$ |
$1$ |
$\Z/3\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.15.2, 3.720.4 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(1.179535\) |
\(0.262119\) |
$[80408,402403732,8094753026048,3388]$ |
$[40204,281112,1967560,19956424,847]$ |
$[105037970421355597057024/847,18267839107785466368/847,454326923025280/121]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -12x^6 - 15x^5 + 9x^4 + 31x^3 + 9x^2 - 15x - 12$ |
847.d.456533.1 |
847.d |
\( 7 \cdot 11^{2} \) |
\( 7^{3} \cdot 11^{3} \) |
$0$ |
$1$ |
$\Z/15\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.15.2, 3.2160.20 |
|
|
$2$ |
\( 3 \) |
\(1.000000\) |
\(9.829455\) |
\(0.262119\) |
$[90952,10132,303847072,1826132]$ |
$[45476,86167752,217689875480,618695823148744,456533]$ |
$[194496275421254111077376/456533,736713878289412204032/41503,10847340081772160/11]$ |
$y^2 + y = -x^6 - 9x^5 - 22x^4 + 3x^3 + 37x^2 - 24x + 4$ |