| 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-a2 |
8.1-a |
$6$ |
$8$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$1.53739$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$223.1882642$ |
0.573311322 |
\( 5088 a^{2} + 8224 a + 3904 \) |
\( \bigl[a^{2} - 1\) , \( -a^{2} + a + 1\) , \( 0\) , \( -122876240093597390564 a^{2} - 143775828060934351842 a + 56622738702290433353\) , \( 1339806177584198660985008156380 a^{2} + 1567689103089350829411708766103 a - 617397594907508652287429548778\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(-122876240093597390564a^{2}-143775828060934351842a+56622738702290433353\right){x}+1339806177584198660985008156380a^{2}+1567689103089350829411708766103a-617397594907508652287429548778$ |
| 16.1-a5 |
16.1-a |
$6$ |
$8$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$1.72566$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$158.7523358$ |
0.815585101 |
\( 5088 a^{2} + 8224 a + 3904 \) |
\( \bigl[a^{2} - 1\) , \( a^{2} - 1\) , \( 0\) , \( 2 a^{2} + 2 a - 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}={x}^{3}+\left(a^{2}-1\right){x}^{2}+\left(2a^{2}+2a-1\right){x}$ |
| 200.2-d5 |
200.2-d |
$6$ |
$8$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
200.2 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$2.62890$ |
$(a^2-a-2), (a^2-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.046818245$ |
$168.1773413$ |
1.941659237 |
\( 5088 a^{2} + 8224 a + 3904 \) |
\( \bigl[a^{2} - 1\) , \( a^{2} - 3\) , \( 0\) , \( -4 a^{2} + 14 a - 3\) , \( 8 a^{2} - 18 a + 6\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-4a^{2}+14a-3\right){x}+8a^{2}-18a+6$ |
| 256.1-b1 |
256.1-b |
$6$ |
$8$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{8} \) |
$2.73932$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$220.5448617$ |
1.133042247 |
\( 5088 a^{2} + 8224 a + 3904 \) |
\( \bigl[a^{2} - 1\) , \( a^{2} - 3\) , \( a^{2} - 1\) , \( -86064964924926 a^{2} - 100703452430598 a + 39659693498548\) , \( -785379897594692293591 a^{2} - 918962405043287659087 a + 361911795882278631324\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-86064964924926a^{2}-100703452430598a+39659693498548\right){x}-785379897594692293591a^{2}-918962405043287659087a+361911795882278631324$ |
| 256.1-e4 |
256.1-e |
$6$ |
$8$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{8} \) |
$2.73932$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$310.0617360$ |
1.592932356 |
\( 5088 a^{2} + 8224 a + 3904 \) |
\( \bigl[a^{2} - 1\) , \( -a^{2} + 2 a + 2\) , \( a^{2} - 1\) , \( -631731729485826 a^{2} - 739180759844258 a + 291109010345492\) , \( 15618492416928874935446 a^{2} + 18274986918519657135933 a - 7197175095639575637344\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{2}+2a+2\right){x}^{2}+\left(-631731729485826a^{2}-739180759844258a+291109010345492\right){x}+15618492416928874935446a^{2}+18274986918519657135933a-7197175095639575637344$ |
| 400.2-a2 |
400.2-a |
$6$ |
$8$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
400.2 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$2.95084$ |
$(a^2-a-2), (a^2-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$81.32192145$ |
1.671155191 |
\( 5088 a^{2} + 8224 a + 3904 \) |
\( \bigl[a^{2} - 1\) , \( -a^{2} + 2 a + 2\) , \( 0\) , \( 2 a^{2} - 3\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}={x}^{3}+\left(-a^{2}+2a+2\right){x}^{2}+\left(2a^{2}-3\right){x}$ |
*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.
