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 |
97.2-a1 |
97.2-a |
$6$ |
$8$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
97.2 |
\( 97 \) |
\( -97 \) |
$1.34080$ |
$(-4a^2+3a+4)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$75.08705405$ |
0.670420125 |
\( -\frac{676992332021380}{97} a^{2} + \frac{373257224900061}{97} a + \frac{1525594015221170}{97} \) |
\( \bigl[a^{2} + a - 1\) , \( 1\) , \( a^{2} + a - 1\) , \( 20 a^{2} + 15 a - 95\) , \( -71 a^{2} - 50 a + 307\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+{x}^{2}+\left(20a^{2}+15a-95\right){x}-71a^{2}-50a+307$ |
97.2-a2 |
97.2-a |
$6$ |
$8$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
97.2 |
\( 97 \) |
\( - 97^{8} \) |
$1.34080$ |
$(-4a^2+3a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.346470439$ |
0.670420125 |
\( -\frac{480678741928115616785}{7837433594376961} a^{2} - \frac{1609238685780030339841}{7837433594376961} a + \frac{1071365947499014693145}{7837433594376961} \) |
\( \bigl[a^{2} + a - 1\) , \( 1\) , \( a^{2} + a - 1\) , \( -20 a^{2} + 10 a - 40\) , \( -128 a^{2} + 26 a - 94\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+{x}^{2}+\left(-20a^{2}+10a-40\right){x}-128a^{2}+26a-94$ |
97.2-a3 |
97.2-a |
$6$ |
$8$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
97.2 |
\( 97 \) |
\( 97^{2} \) |
$1.34080$ |
$(-4a^2+3a+4)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$150.1741081$ |
0.670420125 |
\( -\frac{14931581759}{9409} a^{2} + \frac{8767640324}{9409} a + \frac{36766527484}{9409} \) |
\( \bigl[a^{2} + a - 1\) , \( 1\) , \( a^{2} + a - 1\) , \( -5\) , \( -4 a^{2} - 3 a + 5\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+{x}^{2}-5{x}-4a^{2}-3a+5$ |
97.2-a4 |
97.2-a |
$6$ |
$8$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
97.2 |
\( 97 \) |
\( 97 \) |
$1.34080$ |
$(-4a^2+3a+4)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$300.3482162$ |
0.670420125 |
\( \frac{96611}{97} a^{2} + \frac{4881}{97} a - \frac{152345}{97} \) |
\( \bigl[a^{2} + a - 1\) , \( 1\) , \( a^{2} + a - 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+{x}^{2}$ |
97.2-a5 |
97.2-a |
$6$ |
$8$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
97.2 |
\( 97 \) |
\( 97^{4} \) |
$1.34080$ |
$(-4a^2+3a+4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$18.77176351$ |
0.670420125 |
\( \frac{4015292960676897540}{88529281} a^{2} + \frac{3220015004154662275}{88529281} a - \frac{2228319255078131746}{88529281} \) |
\( \bigl[a^{2} + a - 1\) , \( 1\) , \( a^{2} + a - 1\) , \( -20 a^{2} - 15 a + 5\) , \( -113 a^{2} - 88 a + 63\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+{x}^{2}+\left(-20a^{2}-15a+5\right){x}-113a^{2}-88a+63$ |
97.2-a6 |
97.2-a |
$6$ |
$8$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
97.2 |
\( 97 \) |
\( 97^{2} \) |
$1.34080$ |
$(-4a^2+3a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$2.346470439$ |
0.670420125 |
\( \frac{80074872029715285046852049}{9409} a^{2} + \frac{64215061570372048452672705}{9409} a - \frac{44438201408746080042408713}{9409} \) |
\( \bigl[a^{2} + a - 1\) , \( 1\) , \( a^{2} + a - 1\) , \( -340 a^{2} - 280 a + 210\) , \( -5454 a^{2} - 4362 a + 3052\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+{x}^{2}+\left(-340a^{2}-280a+210\right){x}-5454a^{2}-4362a+3052$ |
*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.