| 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 |
| 97.1-a1 |
97.1-a |
$6$ |
$8$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
97.1 |
\( 97 \) |
\( 97^{2} \) |
$1.34080$ |
$(-3a^2-a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$2.346470439$ |
0.670420125 |
\( \frac{64215061570372048452672705}{9409} a^{2} - \frac{144289933600087333499524754}{9409} a + \frac{51496481080312441598622680}{9409} \) |
\( \bigl[a^{2} - 2\) , \( a^{2} + a - 2\) , \( a^{2} - 1\) , \( -279 a^{2} + 620 a - 191\) , \( -3742 a^{2} + 8446 a - 3024\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(-279a^{2}+620a-191\right){x}-3742a^{2}+8446a-3024$ |
| 97.1-a2 |
97.1-a |
$6$ |
$8$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
97.1 |
\( 97 \) |
\( - 97^{8} \) |
$1.34080$ |
$(-3a^2-a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.346470439$ |
0.670420125 |
\( -\frac{1609238685780030339841}{7837433594376961} a^{2} + \frac{2089917427708145956626}{7837433594376961} a + \frac{1719247149422813799416}{7837433594376961} \) |
\( \bigl[a^{2} - 2\) , \( a^{2} + a - 2\) , \( a^{2} - 1\) , \( 11 a^{2} + 10 a - 91\) , \( 36 a^{2} + 22 a - 296\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(11a^{2}+10a-91\right){x}+36a^{2}+22a-296$ |
| 97.1-a3 |
97.1-a |
$6$ |
$8$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
97.1 |
\( 97 \) |
\( -97 \) |
$1.34080$ |
$(-3a^2-a+7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$75.08705405$ |
0.670420125 |
\( \frac{373257224900061}{97} a^{2} + \frac{303735107121319}{97} a - \frac{201647873721651}{97} \) |
\( \bigl[a^{2} - 2\) , \( a^{2} + a - 2\) , \( a^{2} - 1\) , \( 16 a^{2} - 35 a - 71\) , \( -85 a^{2} + 116 a + 270\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(16a^{2}-35a-71\right){x}-85a^{2}+116a+270$ |
| 97.1-a4 |
97.1-a |
$6$ |
$8$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
97.1 |
\( 97 \) |
\( 97^{4} \) |
$1.34080$ |
$(-3a^2-a+7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$18.77176351$ |
0.670420125 |
\( \frac{3220015004154662275}{88529281} a^{2} - \frac{7235307964831559815}{88529281} a + \frac{2582251662121001059}{88529281} \) |
\( \bigl[a^{2} - 2\) , \( a^{2} + a - 2\) , \( a^{2} - 1\) , \( -14 a^{2} + 35 a - 21\) , \( -53 a^{2} + 116 a - 40\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(-14a^{2}+35a-21\right){x}-53a^{2}+116a-40$ |
| 97.1-a5 |
97.1-a |
$6$ |
$8$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
97.1 |
\( 97 \) |
\( 97^{2} \) |
$1.34080$ |
$(-3a^2-a+7)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$150.1741081$ |
0.670420125 |
\( \frac{8767640324}{9409} a^{2} + \frac{6163941435}{9409} a - \frac{1864276358}{9409} \) |
\( \bigl[a^{2} - 2\) , \( a^{2} + a - 2\) , \( a^{2} - 1\) , \( a^{2} - 6\) , \( -3 a^{2} + 2 a + 5\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(a^{2}-6\right){x}-3a^{2}+2a+5$ |
| 97.1-a6 |
97.1-a |
$6$ |
$8$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
97.1 |
\( 97 \) |
\( 97 \) |
$1.34080$ |
$(-3a^2-a+7)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$300.3482162$ |
0.670420125 |
\( \frac{4881}{97} a^{2} - \frac{101492}{97} a + \frac{35996}{97} \) |
\( \bigl[a^{2} - 2\) , \( a^{2} + a - 2\) , \( a^{2} - 1\) , \( a^{2} - 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(a^{2}-1\right){x}$ |
*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.
