| 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 |
| 392.2-a1 |
392.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-26}) \) |
$2$ |
$[0, 1]$ |
392.2 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{2} \) |
$4.05487$ |
$(2,a), (7,a+3), (7,a+4)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$8.032591436$ |
0.787660393 |
\( \frac{432}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 2\bigr] \) |
${y}^2={x}^3+{x}+2$ |
| 392.2-a2 |
392.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-26}) \) |
$2$ |
$[0, 1]$ |
392.2 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{22} \cdot 7^{8} \) |
$4.05487$ |
$(2,a), (7,a+3), (7,a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.008147859$ |
0.787660393 |
\( \frac{11090466}{2401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -59\) , \( -138\bigr] \) |
${y}^2={x}^3-59{x}-138$ |
| 392.2-a3 |
392.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-26}) \) |
$2$ |
$[0, 1]$ |
392.2 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{4} \) |
$4.05487$ |
$(2,a), (7,a+3), (7,a+4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.016295718$ |
0.787660393 |
\( \frac{740772}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -19\) , \( 30\bigr] \) |
${y}^2={x}^3-19{x}+30$ |
| 392.2-a4 |
392.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-26}) \) |
$2$ |
$[0, 1]$ |
392.2 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{22} \cdot 7^{2} \) |
$4.05487$ |
$(2,a), (7,a+3), (7,a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$2.008147859$ |
0.787660393 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -299\) , \( 1990\bigr] \) |
${y}^2={x}^3-299{x}+1990$ |
| 392.2-b1 |
392.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-26}) \) |
$2$ |
$[0, 1]$ |
392.2 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$4.05487$ |
$(2,a), (7,a+3), (7,a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.069108576$ |
$8.032591436$ |
1.684188965 |
\( \frac{432}{7} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 32\) , \( -10\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+32{x}-10$ |
| 392.2-b2 |
392.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-26}) \) |
$2$ |
$[0, 1]$ |
392.2 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{10} \cdot 7^{8} \) |
$4.05487$ |
$(2,a), (7,a+3), (7,a+4)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.069108576$ |
$2.008147859$ |
1.684188965 |
\( \frac{11090466}{2401} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 17\) , \( 45\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+17{x}+45$ |
| 392.2-b3 |
392.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-26}) \) |
$2$ |
$[0, 1]$ |
392.2 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{4} \) |
$4.05487$ |
$(2,a), (7,a+3), (7,a+4)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.138217153$ |
$4.016295718$ |
1.684188965 |
\( \frac{740772}{49} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 27\) , \( -1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+27{x}-1$ |
| 392.2-b4 |
392.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-26}) \) |
$2$ |
$[0, 1]$ |
392.2 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{10} \cdot 7^{2} \) |
$4.05487$ |
$(2,a), (7,a+3), (7,a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$4.276434307$ |
$2.008147859$ |
1.684188965 |
\( \frac{1443468546}{7} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -43\) , \( -71\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2-43{x}-71$ |
| 392.2-c1 |
392.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{-26}) \) |
$2$ |
$[0, 1]$ |
392.2 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{8} \cdot 5^{12} \cdot 7^{2} \) |
$4.05487$ |
$(2,a), (7,a+3), (7,a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1.854667840$ |
$5.234991156$ |
15.23299876 |
\( \frac{35680}{7} a + \frac{169412}{7} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -13 a - 53\) , \( 42 a + 388\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+\left(-13a-53\right){x}+42a+388$ |
| 392.2-d1 |
392.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{-26}) \) |
$2$ |
$[0, 1]$ |
392.2 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 7^{2} \) |
$4.05487$ |
$(2,a), (7,a+3), (7,a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$5.234991156$ |
2.053332466 |
\( \frac{35680}{7} a + \frac{169412}{7} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -5 a + 34\) , \( 12 a - 115\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+\left(-5a+34\right){x}+12a-115$ |
| 392.2-e1 |
392.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{-26}) \) |
$2$ |
$[0, 1]$ |
392.2 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{2} \) |
$4.05487$ |
$(2,a), (7,a+3), (7,a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$9$ |
\( 2^{2} \) |
$1$ |
$6.395739286$ |
11.28876903 |
\( -\frac{4}{7} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 23\) , \( 1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+23{x}+1$ |
| 392.2-e2 |
392.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{-26}) \) |
$2$ |
$[0, 1]$ |
392.2 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{10} \cdot 7^{4} \) |
$4.05487$ |
$(2,a), (7,a+3), (7,a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$9$ |
\( 2^{3} \) |
$1$ |
$3.197869643$ |
11.28876903 |
\( \frac{3543122}{49} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 13\) , \( 31\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+13{x}+31$ |
| 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 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2-4$ |
| 392.2-f2 |
392.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{-26}) \) |
$2$ |
$[0, 1]$ |
392.2 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{22} \cdot 7^{4} \) |
$4.05487$ |
$(2,a), (7,a+3), (7,a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.425426985$ |
$3.197869643$ |
6.084463343 |
\( \frac{3543122}{49} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -40\) , \( -84\bigr] \) |
${y}^2={x}^3-{x}^2-40{x}-84$ |
| 392.2-g1 |
392.2-g |
$1$ |
$1$ |
\(\Q(\sqrt{-26}) \) |
$2$ |
$[0, 1]$ |
392.2 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{8} \cdot 5^{12} \cdot 7^{2} \) |
$4.05487$ |
$(2,a), (7,a+3), (7,a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1.854667840$ |
$5.234991156$ |
15.23299876 |
\( -\frac{35680}{7} a + \frac{169412}{7} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 13 a - 53\) , \( -42 a + 388\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(-a+1\right){x}^2+\left(13a-53\right){x}-42a+388$ |
| 392.2-h1 |
392.2-h |
$1$ |
$1$ |
\(\Q(\sqrt{-26}) \) |
$2$ |
$[0, 1]$ |
392.2 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 7^{2} \) |
$4.05487$ |
$(2,a), (7,a+3), (7,a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$5.234991156$ |
2.053332466 |
\( -\frac{35680}{7} a + \frac{169412}{7} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 5 a + 34\) , \( -12 a - 115\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+\left(5a+34\right){x}-12a-115$ |
*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.
