| 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-a1 |
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 |
\( -2624 a^{2} + 1536 a + 9024 \) |
\( \bigl[a^{2} - 1\) , \( -1\) , \( a^{2} - a - 2\) , \( 1727261180779898112178031 a^{2} + 2021044966504285468600887 a - 795941171665179475905777\) , \( 279884457042981407569057081184688558284 a^{2} + 327489021002657174715208924802606509852 a - 128973872132688546804017272390232511682\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}-{x}^{2}+\left(1727261180779898112178031a^{2}+2021044966504285468600887a-795941171665179475905777\right){x}+279884457042981407569057081184688558284a^{2}+327489021002657174715208924802606509852a-128973872132688546804017272390232511682$ |
| 16.1-a6 |
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 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$158.7523358$ |
0.815585101 |
\( -2624 a^{2} + 1536 a + 9024 \) |
\( \bigl[a^{2} - 1\) , \( -a^{2} + a + 1\) , \( a^{2} - a - 2\) , \( 8858 a^{2} + 10364 a - 4082\) , \( -102778712 a^{2} - 120259982 a + 47361573\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(8858a^{2}+10364a-4082\right){x}-102778712a^{2}-120259982a+47361573$ |
| 200.2-d6 |
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 |
\( -2624 a^{2} + 1536 a + 9024 \) |
\( \bigl[a^{2} - 1\) , \( a + 1\) , \( a + 1\) , \( 608 a^{2} + 712 a - 279\) , \( 1845556 a^{2} + 2159460 a - 850453\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(608a^{2}+712a-279\right){x}+1845556a^{2}+2159460a-850453$ |
| 256.1-b6 |
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 |
$1$ |
\( 1 \) |
$1$ |
$55.13621542$ |
1.133042247 |
\( -2624 a^{2} + 1536 a + 9024 \) |
\( \bigl[0\) , \( a^{2} - a - 2\) , \( 0\) , \( 102253970213414727 a^{2} + 119645988750577542 a - 47119767273605408\) , \( -4031456994839579610987491418 a^{2} - 4717153351075791871135103011 a + 1857740242006452258727417755\bigr] \) |
${y}^2={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(102253970213414727a^{2}+119645988750577542a-47119767273605408\right){x}-4031456994839579610987491418a^{2}-4717153351075791871135103011a+1857740242006452258727417755$ |
| 256.1-e6 |
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 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$77.51543401$ |
1.592932356 |
\( -2624 a^{2} + 1536 a + 9024 \) |
\( \bigl[0\) , \( a^{2} - a - 1\) , \( 0\) , \( 750561828568228721 a^{2} + 878222252985010170 a - 345867242247645683\) , \( 80171770176002958186701740874 a^{2} + 93807904891829134609275758426 a - 36944043783550265805016258622\bigr] \) |
${y}^2={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(750561828568228721a^{2}+878222252985010170a-345867242247645683\right){x}+80171770176002958186701740874a^{2}+93807904891829134609275758426a-36944043783550265805016258622$ |
| 400.2-a1 |
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 |
\( -2624 a^{2} + 1536 a + 9024 \) |
\( \bigl[a^{2} - 1\) , \( -a^{2} + 1\) , \( a + 1\) , \( 4455 a^{2} + 5213 a - 2052\) , \( -36675517 a^{2} - 42913527 a + 16900486\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+1\right){x}^{2}+\left(4455a^{2}+5213a-2052\right){x}-36675517a^{2}-42913527a+16900486$ |
*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.
