| 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 |
| 169.a.169.1 |
169.a |
\( 13^{2} \) |
\( - 13^{2} \) |
$0$ |
$0$ |
$\Z/19\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$6$ |
$0$ |
2.40.3, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(32.667031\) |
\(0.090490\) |
$[4,793,3757,-21632]$ |
$[1,-33,-43,-283,-169]$ |
$[-1/169,33/169,43/169]$ |
$y^2 + (x^3 + x + 1)y = x^5 + x^4$ |
| 249.a.249.1 |
249.a |
\( 3 \cdot 83 \) |
\( 3 \cdot 83 \) |
$0$ |
$1$ |
$\Z/14\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(25.783703\) |
\(0.131550\) |
$[108,57,2259,-31872]$ |
$[27,28,32,20,-249]$ |
$[-4782969/83,-183708/83,-7776/83]$ |
$y^2 + (x^3 + 1)y = x^2 + x$ |
| 277.a.277.1 |
277.a |
\( 277 \) |
\( 277 \) |
$0$ |
$0$ |
$\Z/15\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(32.205749\) |
\(0.143137\) |
$[64,352,9552,-1108]$ |
$[32,-16,-464,-3776,-277]$ |
$[-33554432/277,524288/277,475136/277]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^2 - x$ |
| 277.a.277.2 |
277.a |
\( 277 \) |
\( 277 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1, 3.80.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(3.578417\) |
\(0.143137\) |
$[4480,1370512,1511819744,-1108]$ |
$[2240,-19352,164384,-1569936,-277]$ |
$[-56394933862400000/277,217505333248000/277,-824813158400/277]$ |
$y^2 + y = x^5 - 9x^4 + 14x^3 - 19x^2 + 11x - 6$ |
| 294.a.294.1 |
294.a |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( - 2 \cdot 3 \cdot 7^{2} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.45.1, 3.720.4 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(21.451533\) |
\(0.148969\) |
$[236,505,18451,37632]$ |
$[59,124,564,4475,294]$ |
$[714924299/294,12733498/147,327214/49]$ |
$y^2 + (x^3 + 1)y = x^4 + x^2$ |
| 295.a.295.1 |
295.a |
\( 5 \cdot 59 \) |
\( - 5 \cdot 59 \) |
$0$ |
$1$ |
$\Z/14\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(29.256600\) |
\(0.149268\) |
$[108,-39,20835,37760]$ |
$[27,32,-256,-1984,295]$ |
$[14348907/295,629856/295,-186624/295]$ |
$y^2 + (x^3 + 1)y = -x^2$ |
| 295.a.295.2 |
295.a |
\( 5 \cdot 59 \) |
\( - 5 \cdot 59 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.597073\) |
\(0.149268\) |
$[198804,305807001,18482629056189,-37760]$ |
$[49701,90182600,203402032096,494095763610824,-295]$ |
$[-303267334973269931148501/295,-2214359494206283568520/59,-502441543825401014496/295]$ |
$y^2 + (x^2 + x + 1)y = x^5 - 40x^3 + 22x^2 + 389x - 608$ |
| 349.a.349.1 |
349.a |
\( 349 \) |
\( 349 \) |
$0$ |
$0$ |
$\Z/13\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,13$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(27.988484\) |
\(0.165612\) |
$[8,208,1464,-1396]$ |
$[4,-34,-124,-413,-349]$ |
$[-1024/349,2176/349,1984/349]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x^2$ |
| 353.a.353.1 |
353.a |
\( 353 \) |
\( -353 \) |
$0$ |
$0$ |
$\Z/11\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,11$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(22.495495\) |
\(0.185913\) |
$[188,817,30871,45184]$ |
$[47,58,256,2167,353]$ |
$[229345007/353,6021734/353,565504/353]$ |
$y^2 + (x^3 + x + 1)y = x^2$ |
| 389.a.389.1 |
389.a |
\( 389 \) |
\( 389 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(19.798620\) |
\(0.197986\) |
$[2440,51100,45041351,1556]$ |
$[1220,53500,2084961,-79649395,389]$ |
$[2702708163200000/389,97147868000000/389,3103255952400/389]$ |
$y^2 + (x^3 + x)y = x^5 - 2x^4 - 8x^3 + 16x + 7$ |
| 389.a.389.2 |
389.a |
\( 389 \) |
\( 389 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(19.798620\) |
\(0.197986\) |
$[16,100,1775,1556]$ |
$[8,-14,-159,-367,389]$ |
$[32768/389,-7168/389,-10176/389]$ |
$y^2 + (x + 1)y = x^5 + 2x^4 + 2x^3 + x^2$ |
| 394.a.394.1 |
394.a |
\( 2 \cdot 197 \) |
\( 2 \cdot 197 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(20.078274\) |
\(0.200783\) |
$[11032,106300,393913607,1576]$ |
$[5516,1250044,371875905,122164372511,394]$ |
$[12960598758485504,532478222573696,28717744887720]$ |
$y^2 + (x^3 + x)y = 2x^5 + x^4 - 12x^3 + 17x - 9$ |
| 448.a.448.2 |
448.a |
\( 2^{6} \cdot 7 \) |
\( - 2^{6} \cdot 7 \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.90.3, 3.2160.5 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(31.171156\) |
\(0.216466\) |
$[828,16635,5308452,56]$ |
$[828,17476,-853888,-253107460,448]$ |
$[6080953884912/7,155007628668/7,-1306723104]$ |
$y^2 + (x^3 + x)y = -2x^4 + 7$ |
| 448.a.448.1 |
448.a |
\( 2^{6} \cdot 7 \) |
\( 2^{6} \cdot 7 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.45.1, 3.2160.5 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(7.792789\) |
\(0.216466\) |
$[828,16635,5308452,56]$ |
$[828,17476,-853888,-253107460,448]$ |
$[6080953884912/7,155007628668/7,-1306723104]$ |
$y^2 + (x^3 + x)y = x^4 - 7$ |
| 461.a.461.1 |
461.a |
\( 461 \) |
\( 461 \) |
$0$ |
$0$ |
$\Z/7\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(12.048435\) |
\(0.245886\) |
$[1176,144,66456,1844]$ |
$[588,14382,467132,16957923,461]$ |
$[70288881159168/461,2923824242304/461,161508086208/461]$ |
$y^2 + x^3y = x^5 - 3x^3 + 3x - 2$ |
| 461.a.461.2 |
461.a |
\( 461 \) |
\( 461 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.245886\) |
\(0.245886\) |
$[80664,166117104,3752725952952,1844]$ |
$[40332,40091742,45075737276,52661714805267,461]$ |
$[106720731303787612818432/461,2630293443843585469056/461,73323359651716069824/461]$ |
$y^2 + y = x^5 - x^4 - 39x^3 + 10x^2 + 272x - 306$ |
| 464.a.464.1 |
464.a |
\( 2^{4} \cdot 29 \) |
\( 2^{4} \cdot 29 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(14.421431\) |
\(0.225335\) |
$[136,280,15060,1856]$ |
$[68,146,-64,-6417,464]$ |
$[90870848/29,2869192/29,-18496/29]$ |
$y^2 + (x + 1)y = -x^6 - 2x^5 - 2x^4 - x^3$ |
