| 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-c4 |
22.1-c |
$6$ |
$8$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( - 2 \cdot 11^{8} \) |
$6.92994$ |
$(-a), (-a^3+2a^2+2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.027949886$ |
$256.4152981$ |
1.087992806 |
\( -\frac{981714842139174225}{428717762} a^{3} + \frac{171035604423335643}{428717762} a^{2} + \frac{2034041293141012467}{214358881} a + \frac{2377646930850683857}{428717762} \) |
\( \bigl[a^{2} - 1\) , \( a^{2} - 2 a - 1\) , \( 0\) , \( 4 a^{3} - 4 a^{2} - 4 a\) , \( 15 a^{3} - 18 a^{2} - a + 12\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}={x}^{3}+\left(a^{2}-2a-1\right){x}^{2}+\left(4a^{3}-4a^{2}-4a\right){x}+15a^{3}-18a^{2}-a+12$ |
| 176.2-a2 |
176.2-a |
$6$ |
$8$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
176.2 |
\( 2^{4} \cdot 11 \) |
\( - 2^{13} \cdot 11^{8} \) |
$8.98702$ |
$(-a), (-a^3+2a^2+2a-1)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$203.8523807$ |
1.934184293 |
\( -\frac{981714842139174225}{428717762} a^{3} + \frac{171035604423335643}{428717762} a^{2} + \frac{2034041293141012467}{214358881} a + \frac{2377646930850683857}{428717762} \) |
\( \bigl[a^{2} - 2\) , \( -a^{3} + 2 a^{2} + 2 a - 2\) , \( a^{3} - 3 a\) , \( 5 a^{3} + 3 a^{2} - 2 a - 6\) , \( -65 a^{3} - 91 a^{2} + 45 a + 61\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-2\right){x}^{2}+\left(5a^{3}+3a^{2}-2a-6\right){x}-65a^{3}-91a^{2}+45a+61$ |
| 242.1-i6 |
242.1-i |
$6$ |
$8$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
242.1 |
\( 2 \cdot 11^{2} \) |
\( - 2 \cdot 11^{14} \) |
$9.35198$ |
$(-a), (-a^3+2a^2+2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$23.80150866$ |
1.806660449 |
\( -\frac{981714842139174225}{428717762} a^{3} + \frac{171035604423335643}{428717762} a^{2} + \frac{2034041293141012467}{214358881} a + \frac{2377646930850683857}{428717762} \) |
\( \bigl[a + 1\) , \( -a^{3} + 2 a^{2} + 2 a - 4\) , \( 0\) , \( 19 a^{3} + 19 a^{2} - 49 a - 52\) , \( -227 a^{3} - 362 a^{2} + 54 a + 126\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-4\right){x}^{2}+\left(19a^{3}+19a^{2}-49a-52\right){x}-227a^{3}-362a^{2}+54a+126$ |
| 704.3-c2 |
704.3-c |
$6$ |
$8$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
704.3 |
\( 2^{6} \cdot 11 \) |
\( - 2^{19} \cdot 11^{8} \) |
$10.68742$ |
$(-a), (-a^3+2a^2+2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.658282403$ |
$59.07353816$ |
2.951734429 |
\( -\frac{981714842139174225}{428717762} a^{3} + \frac{171035604423335643}{428717762} a^{2} + \frac{2034041293141012467}{214358881} a + \frac{2377646930850683857}{428717762} \) |
\( \bigl[a^{3} - 4 a\) , \( -a^{2} + 1\) , \( 0\) , \( 14 a^{3} + 8 a^{2} - 63 a - 79\) , \( 121 a^{3} - 37 a^{2} - 492 a - 225\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}={x}^{3}+\left(-a^{2}+1\right){x}^{2}+\left(14a^{3}+8a^{2}-63a-79\right){x}+121a^{3}-37a^{2}-492a-225$ |
| 704.3-r5 |
704.3-r |
$6$ |
$8$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
704.3 |
\( 2^{6} \cdot 11 \) |
\( - 2^{19} \cdot 11^{8} \) |
$10.68742$ |
$(-a), (-a^3+2a^2+2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$16.17207988$ |
2.455092869 |
\( -\frac{981714842139174225}{428717762} a^{3} + \frac{171035604423335643}{428717762} a^{2} + \frac{2034041293141012467}{214358881} a + \frac{2377646930850683857}{428717762} \) |
\( \bigl[a\) , \( -a^{3} + 3 a + 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -486 a^{3} + 840 a^{2} + 1369 a - 1515\) , \( -7344 a^{3} + 12462 a^{2} + 20884 a - 22065\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{3}+3a+2\right){x}^{2}+\left(-486a^{3}+840a^{2}+1369a-1515\right){x}-7344a^{3}+12462a^{2}+20884a-22065$ |
*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.
