| 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 |
| 256.a.512.1 |
256.a |
\( 2^{8} \) |
\( - 2^{9} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/10\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_4$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$6$ |
$2$ |
2.180.3, 3.540.6 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(26.841829\) |
\(0.134209\) |
$[26,-2,40,2]$ |
$[52,118,-36,-3949,512]$ |
$[742586,129623/4,-1521/8]$ |
$y^2 + y = 2x^5 - 3x^4 + x^3 + x^2 - x$ |
| 576.a.576.1 |
576.a |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{6} \cdot 3^{2} \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_2$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$4$ |
$0$ |
2.180.4, 3.1080.16 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(22.396252\) |
\(0.223963\) |
$[68,124,2616,72]$ |
$[68,110,-36,-3637,576]$ |
$[22717712/9,540430/9,-289]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x$ |
| 4096.b.65536.1 |
4096.b |
\( 2^{12} \) |
\( - 2^{16} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\mathsf{CM})\) |
\(\mathsf{CM}\) |
✓ |
$J(C_2)$ |
|
✓ |
|
$C_4$ |
$GL(2,3)$ |
$4$ |
$4$ |
2.360.2, 3.6480.22 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(12.689987\) |
\(0.793124\) |
$[20,-20,-40,8]$ |
$[80,480,-1280,-83200,65536]$ |
$[50000,3750,-125]$ |
$y^2 = x^5 - x$ |
| 4096.e.524288.1 |
4096.e |
\( 2^{12} \) |
\( - 2^{19} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_4$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$2$ |
$2$ |
2.180.3, 3.540.6 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(7.402544\) |
\(0.925318\) |
$[26,-2,40,2]$ |
$[208,1888,-2304,-1010944,524288]$ |
$[742586,129623/4,-1521/8]$ |
$y^2 = x^5 - 2x^4 - 2x^2 - x$ |
| 6400.f.64000.1 |
6400.f |
\( 2^{8} \cdot 5^{2} \) |
\( - 2^{9} \cdot 5^{3} \) |
$2$ |
$4$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_4$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$16$ |
$0$ |
2.90.6, 3.540.6 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.067032\) |
\(19.455210\) |
\(0.326031\) |
$[154,310,19480,250]$ |
$[308,3126,-164,-2455597,64000]$ |
$[5413568314/125,713561079/500,-243089/1000]$ |
$y^2 + x^3y = -2x^4 - 3x^3 + x^2 + 6x + 4$ |
| 6400.g.64000.1 |
6400.g |
\( 2^{8} \cdot 5^{2} \) |
\( - 2^{9} \cdot 5^{3} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_4$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$2$ |
$2$ |
2.180.3, 3.540.6 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(6.303153\) |
\(1.575788\) |
$[154,310,19480,250]$ |
$[308,3126,-164,-2455597,64000]$ |
$[5413568314/125,713561079/500,-243089/1000]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^6 - x^3 - x - 1$ |
| 12544.d.25088.1 |
12544.d |
\( 2^{8} \cdot 7^{2} \) |
\( - 2^{9} \cdot 7^{2} \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_4$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$12$ |
$0$ |
2.45.1, 3.540.6 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.058077\) |
\(15.061274\) |
\(0.437354\) |
$[74,142,3272,98]$ |
$[148,534,-196,-78541,25088]$ |
$[138687914/49,13524351/196,-1369/8]$ |
$y^2 + (x^3 + x^2 + x + 1)y = x^4 - x^3 + x^2 - x$ |
| 25600.d.128000.1 |
25600.d |
\( 2^{10} \cdot 5^{2} \) |
\( - 2^{10} \cdot 5^{3} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_4$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$2$ |
$2$ |
2.180.3, 3.540.6 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(13.879043\) |
\(1.734880\) |
$[56,-80,-260,500]$ |
$[112,736,-1536,-178432,128000]$ |
$[17210368/125,1009792/125,-18816/125]$ |
$y^2 = x^5 + x^4 + x^2 - x$ |
| 25600.e.128000.1 |
25600.e |
\( 2^{10} \cdot 5^{2} \) |
\( - 2^{10} \cdot 5^{3} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_4$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$2$ |
$2$ |
2.180.3, 3.540.6 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(9.947770\) |
\(1.243471\) |
$[56,-80,-260,500]$ |
$[112,736,-1536,-178432,128000]$ |
$[17210368/125,1009792/125,-18816/125]$ |
$y^2 = x^5 - x^4 - x^2 - x$ |
| 40000.e.200000.1 |
40000.e |
\( 2^{6} \cdot 5^{4} \) |
\( - 2^{6} \cdot 5^{5} \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\mathsf{CM})\) |
\(\mathsf{CM}\) |
✓ |
$J(C_4)$ |
|
✓ |
|
$C_4$ |
$GL(2,3)$ |
$8$ |
$0$ |
2.90.7, 3.3240.15 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.126734\) |
\(11.350269\) |
\(0.719235\) |
$[20,-20,-40,8]$ |
$[100,750,-2500,-203125,200000]$ |
$[50000,3750,-125]$ |
$y^2 + x^3y = x^5 - 5x^3 - 10x^2 - 8x - 2$ |
| 69696.c.627264.1 |
69696.c |
\( 2^{6} \cdot 3^{2} \cdot 11^{2} \) |
\( - 2^{6} \cdot 3^{4} \cdot 11^{2} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_2$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$0$ |
$0$ |
2.180.4, 3.1080.16 |
|
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(7.488051\) |
\(3.744026\) |
$[1220,3580,1448760,78408]$ |
$[1220,59630,3724380,247001675,627264]$ |
$[42229815050000/9801,1691859628750/9801,8837375]$ |
$y^2 + (x^3 + x^2 + x + 1)y = x^6 + 3x^4 - x^3 + 3x^2 - x + 1$ |
| 78400.a.78400.1 |
78400.a |
\( 2^{6} \cdot 5^{2} \cdot 7^{2} \) |
\( - 2^{6} \cdot 5^{2} \cdot 7^{2} \) |
$0$ |
$2$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_2$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$0$ |
$0$ |
2.90.5, 3.1080.16 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(6.009550\) |
\(3.004775\) |
$[452,1276,189752,9800]$ |
$[452,7662,151900,2488139,78400]$ |
$[294789628688/1225,11055476814/1225,395839]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^6 - 3x^4 - x^3 - 3x^2 - x - 1$ |
| 135424.l.270848.1 |
135424.l |
\( 2^{8} \cdot 23^{2} \) |
\( - 2^{9} \cdot 23^{2} \) |
$0$ |
$2$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_4$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$0$ |
$0$ |
2.45.1, 3.540.6 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(5.075262\) |
\(5.075262\) |
$[170,430,23560,1058]$ |
$[340,3670,31740,-669325,270848]$ |
$[8874106250/529,1126919375/2116,108375/8]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^6 - 2x^4 - x^3 - 2x^2 - x - 1$ |
| 193600.d.968000.1 |
193600.d |
\( 2^{6} \cdot 5^{2} \cdot 11^{2} \) |
\( - 2^{6} \cdot 5^{3} \cdot 11^{2} \) |
$0$ |
$2$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_4$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$0$ |
$0$ |
2.45.1, 3.540.6 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(3.888937\) |
\(3.888937\) |
$[292,2380,214520,121000]$ |
$[292,1966,-4356,-1284277,968000]$ |
$[33169145488/15125,764807422/15125,-47961/125]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^6 - x^4 - x^3 - x^2 - x - 1$ |
| 193600.e.968000.1 |
193600.e |
\( 2^{6} \cdot 5^{2} \cdot 11^{2} \) |
\( - 2^{6} \cdot 5^{3} \cdot 11^{2} \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_4$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$8$ |
$0$ |
2.45.1, 3.540.6 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.208207\) |
\(11.078708\) |
\(1.153332\) |
$[292,2380,214520,121000]$ |
$[292,1966,-4356,-1284277,968000]$ |
$[33169145488/15125,764807422/15125,-47961/125]$ |
$y^2 + (x^3 + x^2 + x + 1)y = 2x^4 - x^3 + 2x^2 - x$ |
