| 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 |
| 48672.2-a1 |
48672.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
48672.2 |
\( 2^{5} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 13^{4} \) |
$3.75408$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.065924653$ |
$2.420020004$ |
3.648047302 |
\( \frac{1000000}{507} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -8\) , \( 6\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-8{x}+6$ |
| 48672.2-a2 |
48672.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
48672.2 |
\( 2^{5} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 13^{2} \) |
$3.75408$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.532962326$ |
$2.420020004$ |
3.648047302 |
\( \frac{10648000}{117} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -18\) , \( 36\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-18{x}+36$ |
| 48672.2-b1 |
48672.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
48672.2 |
\( 2^{5} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{8} \cdot 13^{12} \) |
$3.75408$ |
$(a), (-a-1), (a-1), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.250676465$ |
2.127060340 |
\( -\frac{420526439488}{390971529} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -624\) , \( -9486\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-624{x}-9486$ |
| 48672.2-b2 |
48672.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
48672.2 |
\( 2^{5} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{16} \cdot 13^{6} \) |
$3.75408$ |
$(a), (-a-1), (a-1), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.250676465$ |
2.127060340 |
\( \frac{42246001231552}{14414517} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -2902\) , \( 61132\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-2902{x}+61132$ |
| 48672.2-c1 |
48672.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
48672.2 |
\( 2^{5} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{6} \cdot 3^{24} \cdot 13^{2} \) |
$3.75408$ |
$(a), (-a-1), (a-1), (13)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.638503048$ |
$0.717282506$ |
6.648328681 |
\( -\frac{245314376}{6908733} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -26\) , \( 357\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-26{x}+357$ |
| 48672.2-c2 |
48672.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
48672.2 |
\( 2^{5} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{6} \cdot 13^{8} \) |
$3.75408$ |
$(a), (-a-1), (a-1), (13)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$6.554012193$ |
$0.717282506$ |
6.648328681 |
\( \frac{1360251712}{771147} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -92\) , \( -18\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-92{x}-18$ |
| 48672.2-c3 |
48672.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
48672.2 |
\( 2^{5} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{12} \cdot 13^{4} \) |
$3.75408$ |
$(a), (-a-1), (a-1), (13)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.638503048$ |
$0.717282506$ |
6.648328681 |
\( \frac{22235451328}{123201} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -234\) , \( -1296\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-234{x}-1296$ |
| 48672.2-c4 |
48672.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
48672.2 |
\( 2^{5} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{6} \cdot 3^{6} \cdot 13^{2} \) |
$3.75408$ |
$(a), (-a-1), (a-1), (13)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$6.554012193$ |
$0.717282506$ |
6.648328681 |
\( \frac{11339065490696}{351} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -935\) , \( 10868\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-935{x}+10868$ |
| 48672.2-d1 |
48672.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
48672.2 |
\( 2^{5} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{20} \cdot 13^{2} \) |
$3.75408$ |
$(a), (-a-1), (a-1), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.711431615$ |
2.012232477 |
\( \frac{1643032000}{767637} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -98\) , \( -132\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-98{x}-132$ |
| 48672.2-d2 |
48672.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
48672.2 |
\( 2^{5} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{10} \cdot 13^{4} \) |
$3.75408$ |
$(a), (-a-1), (a-1), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.711431615$ |
2.012232477 |
\( \frac{61162984000}{41067} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -328\) , \( 2398\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-328{x}+2398$ |
| 48672.2-e1 |
48672.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
48672.2 |
\( 2^{5} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 13^{4} \) |
$3.75408$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.416607960$ |
$2.047453076$ |
4.825213237 |
\( \frac{778688}{1521} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 8\) , \( 10\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+8{x}+10$ |
| 48672.2-e2 |
48672.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
48672.2 |
\( 2^{5} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{8} \cdot 13^{2} \) |
$3.75408$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.833215920$ |
$2.047453076$ |
4.825213237 |
\( \frac{5088448}{1053} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -14\) , \( -12\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-14{x}-12$ |
| 48672.2-f1 |
48672.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
48672.2 |
\( 2^{5} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 13^{4} \) |
$3.75408$ |
$(a), (-a-1), (a-1), (13)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.462850700$ |
$2.047453076$ |
10.72160659 |
\( \frac{778688}{1521} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 8\) , \( -10\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+8{x}-10$ |
| 48672.2-f2 |
48672.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
48672.2 |
\( 2^{5} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{8} \cdot 13^{2} \) |
$3.75408$ |
$(a), (-a-1), (a-1), (13)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.115712675$ |
$2.047453076$ |
10.72160659 |
\( \frac{5088448}{1053} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -14\) , \( 12\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-14{x}+12$ |
| 48672.2-g1 |
48672.2-g |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
48672.2 |
\( 2^{5} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{20} \cdot 13^{2} \) |
$3.75408$ |
$(a), (-a-1), (a-1), (13)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5^{2} \) |
$0.053908812$ |
$0.711431615$ |
10.84770631 |
\( \frac{1643032000}{767637} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -98\) , \( 132\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-98{x}+132$ |
| 48672.2-g2 |
48672.2-g |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
48672.2 |
\( 2^{5} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{10} \cdot 13^{4} \) |
$3.75408$ |
$(a), (-a-1), (a-1), (13)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5^{2} \) |
$0.215635249$ |
$0.711431615$ |
10.84770631 |
\( \frac{61162984000}{41067} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -328\) , \( -2398\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-328{x}-2398$ |
| 48672.2-h1 |
48672.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
48672.2 |
\( 2^{5} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{6} \cdot 3^{24} \cdot 13^{2} \) |
$3.75408$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$0.390117995$ |
$0.717282506$ |
7.123176829 |
\( -\frac{245314376}{6908733} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -26\) , \( -357\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-26{x}-357$ |
| 48672.2-h2 |
48672.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
48672.2 |
\( 2^{5} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{6} \cdot 13^{8} \) |
$3.75408$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$0.390117995$ |
$0.717282506$ |
7.123176829 |
\( \frac{1360251712}{771147} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -92\) , \( 18\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-92{x}+18$ |
| 48672.2-h3 |
48672.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
48672.2 |
\( 2^{5} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{12} \cdot 13^{4} \) |
$3.75408$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$0.780235990$ |
$0.717282506$ |
7.123176829 |
\( \frac{22235451328}{123201} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -234\) , \( 1296\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-234{x}+1296$ |
| 48672.2-h4 |
48672.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
48672.2 |
\( 2^{5} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{6} \cdot 3^{6} \cdot 13^{2} \) |
$3.75408$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3^{2} \) |
$1.560471980$ |
$0.717282506$ |
7.123176829 |
\( \frac{11339065490696}{351} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -935\) , \( -10867\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-935{x}-10867$ |
| 48672.2-i1 |
48672.2-i |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
48672.2 |
\( 2^{5} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{8} \cdot 13^{12} \) |
$3.75408$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \cdot 3 \) |
$0.497870448$ |
$0.250676465$ |
8.472003886 |
\( -\frac{420526439488}{390971529} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -624\) , \( 9486\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-624{x}+9486$ |
| 48672.2-i2 |
48672.2-i |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
48672.2 |
\( 2^{5} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{16} \cdot 13^{6} \) |
$3.75408$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \cdot 3 \) |
$0.248935224$ |
$0.250676465$ |
8.472003886 |
\( \frac{42246001231552}{14414517} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -2902\) , \( -61132\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-2902{x}-61132$ |
| 48672.2-j1 |
48672.2-j |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
48672.2 |
\( 2^{5} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 13^{4} \) |
$3.75408$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.419382590$ |
$2.420020004$ |
8.280155731 |
\( \frac{1000000}{507} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -8\) , \( -6\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-8{x}-6$ |
| 48672.2-j2 |
48672.2-j |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
48672.2 |
\( 2^{5} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 13^{2} \) |
$3.75408$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.209691295$ |
$2.420020004$ |
8.280155731 |
\( \frac{10648000}{117} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -18\) , \( -36\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-18{x}-36$ |
*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.
