| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 32448.1-a1 |
32448.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32448.1 |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( 2^{16} \cdot 3^{4} \cdot 13^{3} \) |
$2.07729$ |
$(-2a+1), (-4a+1), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.093432923$ |
$1.854159553$ |
3.200636789 |
\( -\frac{29104}{9} a - 3328 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -18 a + 1\) , \( -43 a + 26\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-18a+1\right){x}-43a+26$ |
| 32448.1-a2 |
32448.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32448.1 |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 13^{3} \) |
$2.07729$ |
$(-2a+1), (-4a+1), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.093432923$ |
$3.708319106$ |
3.200636789 |
\( \frac{256}{3} a - \frac{4864}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 2 a - 4\) , \( -3 a + 3\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(2a-4\right){x}-3a+3$ |
| 32448.1-b1 |
32448.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32448.1 |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( 2^{22} \cdot 3 \cdot 13^{8} \) |
$2.07729$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$7.168216973$ |
$0.174282850$ |
2.885128498 |
\( -\frac{1028251680722}{507} a - \frac{94596173570}{507} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 6234 a + 8147\) , \( -488889 a + 581755\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(6234a+8147\right){x}-488889a+581755$ |
| 32448.1-b2 |
32448.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32448.1 |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( 2^{16} \cdot 3^{4} \cdot 13^{8} \) |
$2.07729$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.792054243$ |
$0.697131401$ |
2.885128498 |
\( -\frac{52528}{1521} a + \frac{5072}{507} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -26 a + 27\) , \( -261 a + 451\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-26a+27\right){x}-261a+451$ |
| 32448.1-b3 |
32448.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32448.1 |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( 2^{22} \cdot 3 \cdot 13^{14} \) |
$2.07729$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$7.168216973$ |
$0.174282850$ |
2.885128498 |
\( \frac{2457991737026}{2447192163} a + \frac{3468181544930}{2447192163} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 1274 a + 547\) , \( -537 a - 15509\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(1274a+547\right){x}-537a-15509$ |
| 32448.1-b4 |
32448.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32448.1 |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 13^{7} \) |
$2.07729$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.896027121$ |
$1.394262803$ |
2.885128498 |
\( \frac{539392}{39} a + \frac{478208}{39} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 14 a - 48\) , \( -33 a + 108\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(14a-48\right){x}-33a+108$ |
| 32448.1-b5 |
32448.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32448.1 |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( 2^{20} \cdot 3^{2} \cdot 13^{10} \) |
$2.07729$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$3.584108486$ |
$0.348565700$ |
2.885128498 |
\( -\frac{4035638236}{85683} a + \frac{3926320864}{85683} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 394 a + 507\) , \( -7785 a + 9235\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(394a+507\right){x}-7785a+9235$ |
| 32448.1-b6 |
32448.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32448.1 |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( 2^{20} \cdot 3^{8} \cdot 13^{7} \) |
$2.07729$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.896027121$ |
$0.348565700$ |
2.885128498 |
\( \frac{89672548}{1053} a + \frac{92596592}{1053} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -1086 a + 747\) , \( -6129 a + 13059\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1086a+747\right){x}-6129a+13059$ |
| 32448.1-c1 |
32448.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32448.1 |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( 2^{22} \cdot 3^{3} \cdot 13^{2} \) |
$2.07729$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1.886196087$ |
2.177991638 |
\( -\frac{8878}{9} a + \frac{21986}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -8 a + 16\) , \( 12\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-8a+16\right){x}+12$ |
| 32448.1-d1 |
32448.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32448.1 |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( 2^{16} \cdot 3^{4} \cdot 13^{9} \) |
$2.07729$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.514251334$ |
2.375225169 |
\( -\frac{29104}{9} a - 3328 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 139 a + 127\) , \( -1215 a + 1725\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(139a+127\right){x}-1215a+1725$ |
| 32448.1-d2 |
32448.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32448.1 |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 13^{9} \) |
$2.07729$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.028502668$ |
2.375225169 |
\( \frac{256}{3} a - \frac{4864}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -41 a + 42\) , \( -8 a + 159\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-41a+42\right){x}-8a+159$ |
| 32448.1-e1 |
32448.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32448.1 |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( 2^{16} \cdot 3 \cdot 13^{6} \) |
$2.07729$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.008263852$ |
2.328485625 |
\( \frac{73696}{3} a - \frac{624368}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -125 a + 115\) , \( -107 a + 577\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-125a+115\right){x}-107a+577$ |
| 32448.1-e2 |
32448.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32448.1 |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( 2^{16} \cdot 3 \cdot 13^{6} \) |
$2.07729$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.008263852$ |
2.328485625 |
\( -\frac{73696}{3} a - \frac{550672}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -120 a\) , \( 548 a - 292\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-120a{x}+548a-292$ |
| 32448.1-e3 |
32448.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32448.1 |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( 2^{22} \cdot 3^{16} \cdot 13^{6} \) |
$2.07729$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.252065963$ |
2.328485625 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -235 a + 110\) , \( -6369 a - 2934\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-235a+110\right){x}-6369a-2934$ |
| 32448.1-e4 |
32448.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32448.1 |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 13^{6} \) |
$2.07729$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.016527704$ |
2.328485625 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -10 a + 5\) , \( 6 a + 6\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-10a+5\right){x}+6a+6$ |
| 32448.1-e5 |
32448.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32448.1 |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( 2^{16} \cdot 3^{4} \cdot 13^{6} \) |
$2.07729$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.008263852$ |
2.328485625 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 65 a - 30\) , \( 115 a + 34\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(65a-30\right){x}+115a+34$ |
| 32448.1-e6 |
32448.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32448.1 |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( 2^{20} \cdot 3^{8} \cdot 13^{6} \) |
$2.07729$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.504131926$ |
2.328485625 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 365 a - 170\) , \( -1465 a - 806\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(365a-170\right){x}-1465a-806$ |
| 32448.1-e7 |
32448.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32448.1 |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( 2^{20} \cdot 3^{2} \cdot 13^{6} \) |
$2.07729$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.504131926$ |
2.328485625 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 965 a - 450\) , \( 7471 a + 3226\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(965a-450\right){x}+7471a+3226$ |
| 32448.1-e8 |
32448.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32448.1 |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( 2^{22} \cdot 3^{4} \cdot 13^{6} \) |
$2.07729$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.252065963$ |
2.328485625 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 5765 a - 2690\) , \( -102481 a - 50198\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(5765a-2690\right){x}-102481a-50198$ |
| 32448.1-f1 |
32448.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32448.1 |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( 2^{22} \cdot 3^{3} \cdot 13^{8} \) |
$2.07729$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3 \) |
$1$ |
$0.523136670$ |
1.812198583 |
\( -\frac{8878}{9} a + \frac{21986}{9} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 182 a - 179\) , \( 615 a + 26\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(182a-179\right){x}+615a+26$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
