| 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 |
| 8.1-a6 |
8.1-a |
$6$ |
$8$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{4} \) |
$1.53739$ |
$(a^2-a-2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$223.1882642$ |
0.573311322 |
\( 297852964 a^{2} + 348495840 a - 137248100 \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 1\) , \( a^{2} - 1\) , \( -23137255028952366700772 a^{2} - 27072589446997404913200 a + 10661904569953464468393\) , \( 3529193720251159834920437017851122 a^{2} + 4129461880751340931496180433614334 a - 1626291736297668628974848142500566\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(-23137255028952366700772a^{2}-27072589446997404913200a+10661904569953464468393\right){x}+3529193720251159834920437017851122a^{2}+4129461880751340931496180433614334a-1626291736297668628974848142500566$ |
| 16.1-a4 |
16.1-a |
$6$ |
$8$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{4} \) |
$1.72566$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$39.68808396$ |
0.815585101 |
\( 297852964 a^{2} + 348495840 a - 137248100 \) |
\( \bigl[a^{2} - a - 2\) , \( a^{2} - 2 a - 3\) , \( a + 1\) , \( -119 a^{2} - 139 a + 58\) , \( -1195 a^{2} - 1399 a + 550\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(-119a^{2}-139a+58\right){x}-1195a^{2}-1399a+550$ |
| 200.2-d1 |
200.2-d |
$6$ |
$8$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
200.2 |
\( 2^{3} \cdot 5^{2} \) |
\( - 2^{4} \cdot 5^{6} \) |
$2.62890$ |
$(a^2-a-2), (a^2-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.093636490$ |
$84.08867066$ |
1.941659237 |
\( 297852964 a^{2} + 348495840 a - 137248100 \) |
\( \bigl[a^{2} - a - 2\) , \( 0\) , \( a^{2} - a - 2\) , \( -12 a^{2} + a - 1\) , \( 14 a^{2} + 50 a - 18\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-12a^{2}+a-1\right){x}+14a^{2}+50a-18$ |
| 256.1-b2 |
256.1-b |
$6$ |
$8$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{16} \) |
$2.73932$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$27.56810771$ |
1.133042247 |
\( 297852964 a^{2} + 348495840 a - 137248100 \) |
\( \bigl[a^{2} - 1\) , \( a^{2} - 3\) , \( a^{2} - 1\) , \( -1369726948580196 a^{2} - 1602698992901198 a + 631185419116543\) , \( -50834524782266614880552 a^{2} - 59480790501786385311994 a + 23425114665039070310143\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-1369726948580196a^{2}-1602698992901198a+631185419116543\right){x}-50834524782266614880552a^{2}-59480790501786385311994a+23425114665039070310143$ |
| 256.1-e5 |
256.1-e |
$6$ |
$8$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{16} \) |
$2.73932$ |
$(a^2-a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$155.0308680$ |
1.592932356 |
\( 297852964 a^{2} + 348495840 a - 137248100 \) |
\( \bigl[a^{2} - 1\) , \( -a^{2} + 2 a + 2\) , \( a^{2} - 1\) , \( -10054032728703376 a^{2} - 11764087831951688 a + 4633010154510017\) , \( 1010923243394735375244094 a^{2} + 1182867626112340667548910 a - 465844679290399901815904\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{2}+2a+2\right){x}^{2}+\left(-10054032728703376a^{2}-11764087831951688a+4633010154510017\right){x}+1010923243394735375244094a^{2}+1182867626112340667548910a-465844679290399901815904$ |
| 400.2-a6 |
400.2-a |
$6$ |
$8$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
400.2 |
\( 2^{4} \cdot 5^{2} \) |
\( - 2^{4} \cdot 5^{6} \) |
$2.95084$ |
$(a^2-a-2), (a^2-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$40.66096072$ |
1.671155191 |
\( 297852964 a^{2} + 348495840 a - 137248100 \) |
\( \bigl[a + 1\) , \( -a^{2} + 2\) , \( a + 1\) , \( -61 a^{2} - 70 a + 29\) , \( -459 a^{2} - 537 a + 212\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-61a^{2}-70a+29\right){x}-459a^{2}-537a+212$ |
*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.
