| 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 |
| 22.1-b7 |
22.1-b |
$8$ |
$20$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( - 2^{20} \cdot 11 \) |
$6.92994$ |
$(-a), (-a^3+2a^2+2a-1)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$424.4736992$ |
1.610989990 |
\( \frac{10003437681517215}{11534336} a^{3} - \frac{16802049412165365}{11534336} a^{2} - \frac{14297353230002373}{5767168} a + \frac{29437605898282179}{11534336} \) |
\( \bigl[a^{2} - a - 1\) , \( a^{3} - 4 a - 2\) , \( 0\) , \( 4 a^{3} - 15 a^{2} + 7 a + 9\) , \( 26 a^{3} - 63 a^{2} - 10 a + 33\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}={x}^{3}+\left(a^{3}-4a-2\right){x}^{2}+\left(4a^{3}-15a^{2}+7a+9\right){x}+26a^{3}-63a^{2}-10a+33$ |
| 176.2-c7 |
176.2-c |
$8$ |
$20$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
176.2 |
\( 2^{4} \cdot 11 \) |
\( - 2^{32} \cdot 11 \) |
$8.98702$ |
$(-a), (-a^3+2a^2+2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$82.79759255$ |
1.571193846 |
\( \frac{10003437681517215}{11534336} a^{3} - \frac{16802049412165365}{11534336} a^{2} - \frac{14297353230002373}{5767168} a + \frac{29437605898282179}{11534336} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{2} - a - 2\) , \( a^{2} - a - 2\) , \( -24 a^{3} + 4 a^{2} + 96 a + 53\) , \( -80 a^{3} + 14 a^{2} + 323 a + 180\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-24a^{3}+4a^{2}+96a+53\right){x}-80a^{3}+14a^{2}+323a+180$ |
| 242.1-a8 |
242.1-a |
$8$ |
$20$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
242.1 |
\( 2 \cdot 11^{2} \) |
\( - 2^{20} \cdot 11^{7} \) |
$9.35198$ |
$(-a), (-a^3+2a^2+2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$0.198661097$ |
$141.1320749$ |
2.128191031 |
\( \frac{10003437681517215}{11534336} a^{3} - \frac{16802049412165365}{11534336} a^{2} - \frac{14297353230002373}{5767168} a + \frac{29437605898282179}{11534336} \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 2\) , \( a^{3} - 4 a - 1\) , \( 104 a^{3} - 271 a^{2} - 13 a + 144\) , \( -1243 a^{3} + 3108 a^{2} + 267 a - 1642\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(104a^{3}-271a^{2}-13a+144\right){x}-1243a^{3}+3108a^{2}+267a-1642$ |
| 704.3-g1 |
704.3-g |
$8$ |
$20$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
704.3 |
\( 2^{6} \cdot 11 \) |
\( - 2^{38} \cdot 11 \) |
$10.68742$ |
$(-a), (-a^3+2a^2+2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$0.711449819$ |
$64.66980634$ |
3.492350992 |
\( \frac{10003437681517215}{11534336} a^{3} - \frac{16802049412165365}{11534336} a^{2} - \frac{14297353230002373}{5767168} a + \frac{29437605898282179}{11534336} \) |
\( \bigl[a^{2} - 2\) , \( -a^{3} + 4 a + 1\) , \( a\) , \( -22 a^{3} - 3 a^{2} + 74 a + 42\) , \( 43 a^{3} + 14 a^{2} - 134 a - 85\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+4a+1\right){x}^{2}+\left(-22a^{3}-3a^{2}+74a+42\right){x}+43a^{3}+14a^{2}-134a-85$ |
| 704.3-n1 |
704.3-n |
$8$ |
$20$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
704.3 |
\( 2^{6} \cdot 11 \) |
\( - 2^{38} \cdot 11 \) |
$10.68742$ |
$(-a), (-a^3+2a^2+2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$89.23654964$ |
1.693381574 |
\( \frac{10003437681517215}{11534336} a^{3} - \frac{16802049412165365}{11534336} a^{2} - \frac{14297353230002373}{5767168} a + \frac{29437605898282179}{11534336} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{3} - a^{2} - 3 a + 1\) , \( a^{3} - 4 a\) , \( 29 a^{3} - 77 a^{2} + 43\) , \( 186 a^{3} - 462 a^{2} - 50 a + 237\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+1\right){x}^{2}+\left(29a^{3}-77a^{2}+43\right){x}+186a^{3}-462a^{2}-50a+237$ |
*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.
