| 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 |
| 3136.2-b1 |
3136.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3136.2 |
\( 2^{6} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{2} \) |
$1.15823$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.197869643$ |
1.846290899 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}-4$ |
| 392.1-a1 |
392.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{2} \) |
$0.79523$ |
$(a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.059979974$ |
$6.395739286$ |
0.767232560 |
\( -\frac{4}{7} \) |
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i\) , \( 0\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}-i{x}$ |
| 448.4-b1 |
448.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
448.4 |
\( 2^{6} \cdot 7 \) |
\( 2^{20} \cdot 7^{2} \) |
$1.08769$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3.197869643$ |
1.208681114 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-4$ |
| 392.1-b1 |
392.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{2} \) |
$1.12462$ |
$(a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$6.395739286$ |
2.261235310 |
\( -\frac{4}{7} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 1\) , \( 1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+{x}+1$ |
| 3136.1-b1 |
3136.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3136.1 |
\( 2^{6} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{2} \) |
$2.21783$ |
$(2), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.124808819$ |
$3.197869643$ |
4.097455728 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-4$ |
| 3136.2-a1 |
3136.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-19}) \) |
$2$ |
$[0, 1]$ |
3136.2 |
\( 2^{6} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{2} \) |
$2.91480$ |
$(-a-1), (a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.197869643$ |
0.733641611 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 392.2-d1 |
392.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
392.2 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{2} \) |
$1.77818$ |
$(2,a+1), (7,a+3), (7,a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.395739286$ |
2.860261562 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 392.2-d1 |
392.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
392.2 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{2} \) |
$1.94790$ |
$(2,a), (a+1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.053535765$ |
$6.395739286$ |
2.750834171 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 3136.11-a1 |
3136.11-a |
$2$ |
$2$ |
\(\Q(\sqrt{-31}) \) |
$2$ |
$[0, 1]$ |
3136.11 |
\( 2^{6} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{2} \) |
$3.72317$ |
$(2,a), (2,a+1), (7,a+2), (7,a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.925974838$ |
$3.197869643$ |
2.127350680 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 448.1-d1 |
448.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
448.1 |
\( 2^{6} \cdot 7 \) |
\( 2^{20} \cdot 7^{2} \) |
$2.43216$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.703452097$ |
$3.197869643$ |
5.845281140 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 392.2-a1 |
392.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
392.2 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{2} \) |
$2.51472$ |
$(2,a), (7,a+2), (7,a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.501182364$ |
$6.395739286$ |
3.036156865 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 3136.1-b1 |
3136.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-43}) \) |
$2$ |
$[0, 1]$ |
3136.1 |
\( 2^{6} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{2} \) |
$4.38497$ |
$(2), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$6.338746832$ |
$3.197869643$ |
6.182440292 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 392.2-d1 |
392.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
392.2 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{2} \) |
$2.86722$ |
$(2,a+1), (7,a+1), (7,a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.395739286$ |
1.773858918 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 56.1-d1 |
56.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
56.1 |
\( 2^{3} \cdot 7 \) |
\( 2^{20} \cdot 7^{2} \) |
$1.82928$ |
$(2,a), (7,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.395739286$ |
1.709333224 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 3136.1-b1 |
3136.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
3136.1 |
\( 2^{6} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{2} \) |
$5.47356$ |
$(2), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$8.292842116$ |
$3.197869643$ |
6.479727582 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 392.2-f1 |
392.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
392.2 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{2} \) |
$3.27880$ |
$(2,a+1), (7,a+2), (7,a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$6.395739286$ |
6.204778502 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 56.1-g1 |
56.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{-21}) \) |
$2$ |
$[0, 1]$ |
56.1 |
\( 2^{3} \cdot 7 \) |
\( 2^{20} \cdot 7^{2} \) |
$2.24040$ |
$(2,a+1), (7,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.513087707$ |
$6.395739286$ |
2.864393675 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 392.1-c1 |
392.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{2} \) |
$3.72994$ |
$(2,a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$6.395739286$ |
2.727152395 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 448.1-a1 |
448.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
448.1 |
\( 2^{6} \cdot 7 \) |
\( 2^{20} \cdot 7^{2} \) |
$3.92174$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.026676007$ |
$3.197869643$ |
2.717592766 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 392.2-f1 |
392.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{-26}) \) |
$2$ |
$[0, 1]$ |
392.2 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{2} \) |
$4.05487$ |
$(2,a), (7,a+3), (7,a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$4.850853970$ |
$6.395739286$ |
6.084463343 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 448.4-d1 |
448.4-d |
$2$ |
$2$ |
\(\Q(\sqrt{-119}) \) |
$2$ |
$[0, 1]$ |
448.4 |
\( 2^{6} \cdot 7 \) |
\( 2^{20} \cdot 7^{2} \) |
$4.48468$ |
$(2,a), (2,a+1), (7,a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$6.395739286$ |
1.172592918 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 392.1-g1 |
392.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{2} \) |
$4.35563$ |
$(2,a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$6.395739286$ |
2.335393786 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 3136.1-b1 |
3136.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
3136.1 |
\( 2^{6} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{2} \) |
$8.53741$ |
$(2), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$16.48568452$ |
$3.197869643$ |
8.258552515 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 56.1-e1 |
56.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-42}) \) |
$2$ |
$[0, 1]$ |
56.1 |
\( 2^{3} \cdot 7 \) |
\( 2^{20} \cdot 7^{2} \) |
$3.16840$ |
$(2,a), (7,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$6.395739286$ |
3.947535989 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 56.1-h1 |
56.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{-70}) \) |
$2$ |
$[0, 1]$ |
56.1 |
\( 2^{3} \cdot 7 \) |
\( 2^{20} \cdot 7^{2} \) |
$4.09039$ |
$(2,a), (7,a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.395355006$ |
$6.395739286$ |
7.324392531 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 56.1-h1 |
56.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{-77}) \) |
$2$ |
$[0, 1]$ |
56.1 |
\( 2^{3} \cdot 7 \) |
\( 2^{20} \cdot 7^{2} \) |
$4.29004$ |
$(2,a+1), (7,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$4.424208894$ |
$6.395739286$ |
12.89855338 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 56.1-m1 |
56.1-m |
$2$ |
$2$ |
\(\Q(\sqrt{-105}) \) |
$2$ |
$[0, 1]$ |
56.1 |
\( 2^{3} \cdot 7 \) |
\( 2^{20} \cdot 7^{2} \) |
$5.00968$ |
$(2,a+1), (7,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.598379946$ |
$6.395739286$ |
6.487221842 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 56.1-g1 |
56.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{-133}) \) |
$2$ |
$[0, 1]$ |
56.1 |
\( 2^{3} \cdot 7 \) |
\( 2^{20} \cdot 7^{2} \) |
$5.63821$ |
$(2,a+1), (7,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.972773873$ |
$12.79147857$ |
6.594574795 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 56.1-b1 |
56.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-154}) \) |
$2$ |
$[0, 1]$ |
56.1 |
\( 2^{3} \cdot 7 \) |
\( 2^{20} \cdot 7^{2} \) |
$6.06703$ |
$(2,a), (7,a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.271814006$ |
$12.79147857$ |
6.744953969 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 56.1-g1 |
56.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{-161}) \) |
$2$ |
$[0, 1]$ |
56.1 |
\( 2^{3} \cdot 7 \) |
\( 2^{20} \cdot 7^{2} \) |
$6.20338$ |
$(2,a+1), (7,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1.009721791$ |
$12.79147857$ |
8.143282960 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 56.1-h1 |
56.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{-182}) \) |
$2$ |
$[0, 1]$ |
56.1 |
\( 2^{3} \cdot 7 \) |
\( 2^{20} \cdot 7^{2} \) |
$6.59555$ |
$(2,a), (7,a)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$12.79147857$ |
7.585339801 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 56.1-n1 |
56.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{-210}) \) |
$2$ |
$[0, 1]$ |
56.1 |
\( 2^{3} \cdot 7 \) |
\( 2^{20} \cdot 7^{2} \) |
$7.08476$ |
$(2,a), (7,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$12.79147857$ |
1.765391763 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 56.1-g1 |
56.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{-217}) \) |
$2$ |
$[0, 1]$ |
56.1 |
\( 2^{3} \cdot 7 \) |
\( 2^{20} \cdot 7^{2} \) |
$7.20187$ |
$(2,a+1), (7,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$5.305179352$ |
$12.79147857$ |
9.213421652 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 56.1-g1 |
56.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{-238}) \) |
$2$ |
$[0, 1]$ |
56.1 |
\( 2^{3} \cdot 7 \) |
\( 2^{20} \cdot 7^{2} \) |
$7.54230$ |
$(2,a), (7,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$12.79147857$ |
1.658296808 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 3136.1-d1 |
3136.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
3136.1 |
\( 2^{6} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{2} \) |
$1.49526$ |
$(2), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.594960974$ |
0.803857711 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-4$ |
| 392.1-c1 |
392.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{2} \) |
$1.12462$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$7.189921948$ |
1.271010641 |
\( -\frac{4}{7} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -1\) , \( -1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-{x}-1$ |
| 392.1-b1 |
392.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{2} \) |
$1.37737$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.189921948$ |
2.075551686 |
\( -\frac{4}{7} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -a + 1\) , \( -8 a - 13\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+1\right){x}-8a-13$ |
| 448.1-h1 |
448.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
448.1 |
\( 2^{6} \cdot 7 \) |
\( 2^{20} \cdot 7^{2} \) |
$1.88394$ |
$(a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.594960974$ |
0.784484799 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-4$ |
| 392.1-b1 |
392.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{2} \) |
$1.94790$ |
$(-a+2), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.747807462$ |
$7.189921948$ |
2.565146328 |
\( -\frac{4}{7} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -2 a - 2\) , \( -100 a - 244\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a-2\right){x}-100a-244$ |
| 56.1-c1 |
56.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
56.1 |
\( 2^{3} \cdot 7 \) |
\( 2^{8} \cdot 7^{2} \) |
$1.29349$ |
$(a+3), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$7.189921948$ |
2.717535060 |
\( -\frac{4}{7} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -2 a - 4\) , \( -396 a - 1048\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-2a-4\right){x}-396a-1048$ |
| 392.1-a1 |
392.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{2} \) |
$2.51472$ |
$(2,a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$5.201719010$ |
$7.189921948$ |
5.913451901 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-4$ |
| 392.1-d1 |
392.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{2} \) |
$2.63746$ |
$(a+3), (a+2), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.866870531$ |
$7.189921948$ |
1.879239242 |
\( -\frac{4}{7} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 9 a - 3\) , \( 612 a - 2003\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(9a-3\right){x}+612a-2003$ |
| 56.1-c1 |
56.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
56.1 |
\( 2^{3} \cdot 7 \) |
\( 2^{8} \cdot 7^{2} \) |
$1.82928$ |
$(-a+4), (-2a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.844493815$ |
$7.189921948$ |
1.622768733 |
\( -\frac{4}{7} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 7 a - 33\) , \( 1856 a - 6948\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(7a-33\right){x}+1856a-6948$ |
*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.
