| 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-b2 |
22.1-b |
$8$ |
$20$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( - 2^{5} \cdot 11^{4} \) |
$6.92994$ |
$(-a), (-a^3+2a^2+2a-1)$ |
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 |
\( \frac{19492220557608647265}{468512} a^{3} + \frac{26555029218814954293}{468512} a^{2} - \frac{7618439534802966603}{234256} a - \frac{16502468789812849155}{468512} \) |
\( \bigl[a^{3} - 4 a - 1\) , \( -a^{3} + 2 a^{2} + 3 a - 4\) , \( a^{2} - 2\) , \( 9 a^{3} + 8 a^{2} - 59 a - 35\) , \( -37 a^{3} + 17 a^{2} + 136 a + 71\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-4\right){x}^{2}+\left(9a^{3}+8a^{2}-59a-35\right){x}-37a^{3}+17a^{2}+136a+71$ |
| 176.2-c5 |
176.2-c |
$8$ |
$20$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
176.2 |
\( 2^{4} \cdot 11 \) |
\( - 2^{17} \cdot 11^{4} \) |
$8.98702$ |
$(-a), (-a^3+2a^2+2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{3} \) |
$1$ |
$41.39879627$ |
1.571193846 |
\( \frac{19492220557608647265}{468512} a^{3} + \frac{26555029218814954293}{468512} a^{2} - \frac{7618439534802966603}{234256} a - \frac{16502468789812849155}{468512} \) |
\( \bigl[a\) , \( -a^{2} + 3\) , \( a^{3} - 3 a\) , \( -6 a^{3} + 9 a^{2} - 6 a - 21\) , \( -14 a^{3} - 11 a^{2} + 31 a + 19\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-6a^{3}+9a^{2}-6a-21\right){x}-14a^{3}-11a^{2}+31a+19$ |
| 242.1-a3 |
242.1-a |
$8$ |
$20$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
242.1 |
\( 2 \cdot 11^{2} \) |
\( - 2^{5} \cdot 11^{10} \) |
$9.35198$ |
$(-a), (-a^3+2a^2+2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$4$ |
\( 2^{2} \) |
$0.794644390$ |
$8.820754682$ |
2.128191031 |
\( \frac{19492220557608647265}{468512} a^{3} + \frac{26555029218814954293}{468512} a^{2} - \frac{7618439534802966603}{234256} a - \frac{16502468789812849155}{468512} \) |
\( \bigl[a^{2} - a - 1\) , \( a^{3} - 4 a - 2\) , \( a^{3} - a^{2} - 2 a + 1\) , \( 165 a^{3} - 22 a^{2} - 727 a - 475\) , \( 1935 a^{3} - 379 a^{2} - 8181 a - 4836\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{3}-a^{2}-2a+1\right){y}={x}^{3}+\left(a^{3}-4a-2\right){x}^{2}+\left(165a^{3}-22a^{2}-727a-475\right){x}+1935a^{3}-379a^{2}-8181a-4836$ |
| 704.3-g4 |
704.3-g |
$8$ |
$20$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
704.3 |
\( 2^{6} \cdot 11 \) |
\( - 2^{23} \cdot 11^{4} \) |
$10.68742$ |
$(-a), (-a^3+2a^2+2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$0.711449819$ |
$64.66980634$ |
3.492350992 |
\( \frac{19492220557608647265}{468512} a^{3} + \frac{26555029218814954293}{468512} a^{2} - \frac{7618439534802966603}{234256} a - \frac{16502468789812849155}{468512} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{2} - a - 2\) , \( a^{2} - 2\) , \( -24 a^{3} - 2 a^{2} + 5 a - 6\) , \( 110 a^{3} + 138 a^{2} - 95 a - 95\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-24a^{3}-2a^{2}+5a-6\right){x}+110a^{3}+138a^{2}-95a-95$ |
| 704.3-n2 |
704.3-n |
$8$ |
$20$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
704.3 |
\( 2^{6} \cdot 11 \) |
\( - 2^{23} \cdot 11^{4} \) |
$10.68742$ |
$(-a), (-a^3+2a^2+2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$4$ |
\( 2^{3} \) |
$1$ |
$11.15456870$ |
1.693381574 |
\( \frac{19492220557608647265}{468512} a^{3} + \frac{26555029218814954293}{468512} a^{2} - \frac{7618439534802966603}{234256} a - \frac{16502468789812849155}{468512} \) |
\( \bigl[a^{3} - 4 a\) , \( -a^{2} + 2 a + 3\) , \( a^{2} - a - 2\) , \( -86 a^{3} + 137 a^{2} + 236 a - 245\) , \( -361 a^{3} + 564 a^{2} + 986 a - 1035\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(-86a^{3}+137a^{2}+236a-245\right){x}-361a^{3}+564a^{2}+986a-1035$ |
*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.
