| 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 |
| 15360.a.15360.1 |
15360.a |
\( 2^{10} \cdot 3 \cdot 5 \) |
\( 2^{10} \cdot 3 \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.270.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(14.071690\) |
\(0.879481\) |
$[432,312,44172,60]$ |
$[864,30272,1378560,68670464,15360]$ |
$[\frac{156728328192}{5},\frac{6355666944}{5},66998016]$ |
$y^2 = x^5 + 7x^4 + 14x^3 + 7x^2 + x$ |
| 15360.b.15360.1 |
15360.b |
\( 2^{10} \cdot 3 \cdot 5 \) |
\( 2^{10} \cdot 3 \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.270.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(20.043090\) |
\(1.252693\) |
$[432,312,44172,60]$ |
$[864,30272,1378560,68670464,15360]$ |
$[\frac{156728328192}{5},\frac{6355666944}{5},66998016]$ |
$y^2 = x^5 - 7x^4 + 14x^3 - 7x^2 + x$ |
| 15360.c.61440.1 |
15360.c |
\( 2^{10} \cdot 3 \cdot 5 \) |
\( - 2^{12} \cdot 3 \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(10.497803\) |
\(1.312225\) |
$[34,-68,-48,240]$ |
$[68,374,-2356,-75021,61440]$ |
$[\frac{1419857}{60},\frac{918731}{480},-\frac{170221}{960}]$ |
$y^2 = x^5 - x^3 - 2x^2 - x$ |
| 15360.d.61440.1 |
15360.d |
\( 2^{10} \cdot 3 \cdot 5 \) |
\( - 2^{12} \cdot 3 \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(9.144407\) |
\(1.143051\) |
$[66,-12,744,240]$ |
$[132,758,-1140,-181261,61440]$ |
$[\frac{13045131}{20},\frac{4540041}{160},-\frac{20691}{64}]$ |
$y^2 = x^5 + x^4 - x^3 - 3x^2 - 3x - 1$ |
| 15360.d.983040.1 |
15360.d |
\( 2^{10} \cdot 3 \cdot 5 \) |
\( - 2^{16} \cdot 3 \cdot 5 \) |
$0$ |
$4$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.270.2 |
✓ |
✓ |
$4$ |
\( 1 \) |
\(1.000000\) |
\(4.572203\) |
\(1.143051\) |
$[11640,897,3480045,120]$ |
$[46560,90316832,233570058240,679472942284544,983040]$ |
$[222583859461440000,9273345076342800,515076721401600]$ |
$y^2 = 2x^6 + 15x^4 + 37x^2 + 30$ |
| 15360.d.983040.2 |
15360.d |
\( 2^{10} \cdot 3 \cdot 5 \) |
\( 2^{16} \cdot 3 \cdot 5 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.270.2 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(9.144407\) |
\(1.143051\) |
$[11640,897,3480045,120]$ |
$[46560,90316832,233570058240,679472942284544,983040]$ |
$[222583859461440000,9273345076342800,515076721401600]$ |
$y^2 = 2x^6 - 15x^4 + 37x^2 - 30$ |
| 15360.e.61440.1 |
15360.e |
\( 2^{10} \cdot 3 \cdot 5 \) |
\( - 2^{12} \cdot 3 \cdot 5 \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.593330\) |
\(15.117118\) |
\(1.121180\) |
$[34,-68,-48,240]$ |
$[68,374,-2356,-75021,61440]$ |
$[\frac{1419857}{60},\frac{918731}{480},-\frac{170221}{960}]$ |
$y^2 = x^5 - x^3 + 2x^2 - x$ |
| 15360.e.245760.1 |
15360.e |
\( 2^{10} \cdot 3 \cdot 5 \) |
\( 2^{14} \cdot 3 \cdot 5 \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.90.6 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.593330\) |
\(15.117118\) |
\(1.121180\) |
$[2812,3283,3020202,30]$ |
$[11248,5236544,3231738880,2232301464576,245760]$ |
$[\frac{10988960165359552}{15},\frac{454831715777072}{15},\frac{4991107625456}{3}]$ |
$y^2 + x^3y = 2x^5 - 18x^3 + 11x^2 + 28x - 24$ |
| 15360.f.61440.1 |
15360.f |
\( 2^{10} \cdot 3 \cdot 5 \) |
\( - 2^{12} \cdot 3 \cdot 5 \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.180.3, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.517860\) |
\(16.674835\) |
\(1.079403\) |
$[66,-12,744,240]$ |
$[132,758,-1140,-181261,61440]$ |
$[\frac{13045131}{20},\frac{4540041}{160},-\frac{20691}{64}]$ |
$y^2 = x^5 - x^4 - x^3 + 3x^2 - 3x + 1$ |
| 15360.f.983040.2 |
15360.f |
\( 2^{10} \cdot 3 \cdot 5 \) |
\( - 2^{16} \cdot 3 \cdot 5 \) |
$1$ |
$4$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.270.2 |
|
|
$2$ |
\( 1 \) |
\(2.071439\) |
\(4.168709\) |
\(1.079403\) |
$[11640,897,3480045,120]$ |
$[46560,90316832,233570058240,679472942284544,983040]$ |
$[222583859461440000,9273345076342800,515076721401600]$ |
$y^2 = -2x^6 - 15x^4 - 37x^2 - 30$ |
| 15360.f.983040.1 |
15360.f |
\( 2^{10} \cdot 3 \cdot 5 \) |
\( 2^{16} \cdot 3 \cdot 5 \) |
$1$ |
$4$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.270.2 |
|
|
$2$ |
\( 2 \) |
\(0.517860\) |
\(8.337418\) |
\(1.079403\) |
$[11640,897,3480045,120]$ |
$[46560,90316832,233570058240,679472942284544,983040]$ |
$[222583859461440000,9273345076342800,515076721401600]$ |
$y^2 = 30x^6 - 37x^4 + 15x^2 - 2$ |
| 15360.g.61440.1 |
15360.g |
\( 2^{10} \cdot 3 \cdot 5 \) |
\( 2^{12} \cdot 3 \cdot 5 \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.258739\) |
\(17.143200\) |
\(1.108905\) |
$[278,640,60792,240]$ |
$[556,11174,229156,638115,61440]$ |
$[\frac{51888844699}{60},\frac{15004553353}{480},\frac{1106880769}{960}]$ |
$y^2 = x^5 + 3x^4 - x^3 - 4x^2 + 2x$ |
| 15360.h.184320.1 |
15360.h |
\( 2^{10} \cdot 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{2} \cdot 5 \) |
$1$ |
$4$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$4$ |
2.360.2, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.516278\) |
\(17.101360\) |
\(1.103633\) |
$[390,852,105720,720]$ |
$[780,23078,838980,30452579,184320]$ |
$[\frac{6265569375}{4},\frac{1901338725}{32},\frac{177234525}{64}]$ |
$y^2 = 2x^5 - x^4 - 5x^3 + 3x + 1$ |
| 15360.i.184320.1 |
15360.i |
\( 2^{10} \cdot 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{2} \cdot 5 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$4$ |
2.360.2, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(10.695870\) |
\(1.336984\) |
$[390,852,105720,720]$ |
$[780,23078,838980,30452579,184320]$ |
$[\frac{6265569375}{4},\frac{1901338725}{32},\frac{177234525}{64}]$ |
$y^2 = 2x^5 + x^4 - 5x^3 + 3x - 1$ |
| 15360.j.491520.1 |
15360.j |
\( 2^{10} \cdot 3 \cdot 5 \) |
\( - 2^{15} \cdot 3 \cdot 5 \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.6, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.891621\) |
\(5.185211\) |
\(1.155811\) |
$[5856,573,1118244,60]$ |
$[23424,22855712,29727006720,43485458595584,491520]$ |
$[\frac{71735496284307456}{5},\frac{2988179922511872}{5},33184257601536]$ |
$y^2 + x^3y = 6x^4 + 47x^2 + 120$ |
| 15360.j.491520.2 |
15360.j |
\( 2^{10} \cdot 3 \cdot 5 \) |
\( 2^{15} \cdot 3 \cdot 5 \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.6, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.891621\) |
\(10.370422\) |
\(1.155811\) |
$[5856,573,1118244,60]$ |
$[23424,22855712,29727006720,43485458595584,491520]$ |
$[\frac{71735496284307456}{5},\frac{2988179922511872}{5},33184257601536]$ |
$y^2 + x^3y = -6x^4 + 47x^2 - 120$ |
