| 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 |
| 2.2-a8 |
2.2-a |
$8$ |
$16$ |
3.3.316.1 |
$3$ |
$[3, 0]$ |
2.2 |
\( 2 \) |
\( 2^{2} \) |
$1.78301$ |
$(-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$21.43466163$ |
0.602896961 |
\( \frac{8525185037}{4} a^{2} - \frac{12150636535}{2} a + \frac{5069473275}{2} \) |
\( \bigl[1\) , \( -a^{2} + a + 3\) , \( 1\) , \( 237250327 a^{2} - 125580532 a - 1008109982\) , \( 2909065137552 a^{2} - 1539816409981 a - 12361026604032\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(237250327a^{2}-125580532a-1008109982\right){x}+2909065137552a^{2}-1539816409981a-12361026604032$ |
| 16.5-b5 |
16.5-b |
$8$ |
$16$ |
3.3.316.1 |
$3$ |
$[3, 0]$ |
16.5 |
\( 2^{4} \) |
\( 2^{14} \) |
$2.52156$ |
$(-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$200.5904149$ |
0.705255777 |
\( \frac{8525185037}{4} a^{2} - \frac{12150636535}{2} a + \frac{5069473275}{2} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + a + 2\) , \( 0\) , \( 18623821 a^{2} - 9857898 a - 79135231\) , \( -63948294020 a^{2} + 33848892296 a + 271725288464\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(18623821a^{2}-9857898a-79135231\right){x}-63948294020a^{2}+33848892296a+271725288464$ |
| 32.1-c6 |
32.1-c |
$8$ |
$16$ |
3.3.316.1 |
$3$ |
$[3, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{14} \) |
$2.83035$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.132082328$ |
$121.2502537$ |
1.351372542 |
\( \frac{8525185037}{4} a^{2} - \frac{12150636535}{2} a + \frac{5069473275}{2} \) |
\( \bigl[a\) , \( a^{2} + a - 2\) , \( a^{2} - 2\) , \( 30392171 a^{2} - 16087094 a - 129140630\) , \( -133378539946 a^{2} + 70599472536 a + 566744160836\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(30392171a^{2}-16087094a-129140630\right){x}-133378539946a^{2}+70599472536a+566744160836$ |
| 64.7-a7 |
64.7-a |
$8$ |
$16$ |
3.3.316.1 |
$3$ |
$[3, 0]$ |
64.7 |
\( 2^{6} \) |
\( 2^{20} \) |
$3.17696$ |
$(-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$28.64153339$ |
1.611212134 |
\( \frac{8525185037}{4} a^{2} - \frac{12150636535}{2} a + \frac{5069473275}{2} \) |
\( \bigl[a + 1\) , \( -a^{2} + 2\) , \( a + 1\) , \( 494267 a^{2} - 261626 a - 2100214\) , \( 276978244 a^{2} - 146609178 a - 1176919487\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(494267a^{2}-261626a-2100214\right){x}+276978244a^{2}-146609178a-1176919487$ |
| 64.7-d2 |
64.7-d |
$8$ |
$16$ |
3.3.316.1 |
$3$ |
$[3, 0]$ |
64.7 |
\( 2^{6} \) |
\( 2^{20} \) |
$3.17696$ |
$(-a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.620528254$ |
$37.52930762$ |
2.565930457 |
\( \frac{8525185037}{4} a^{2} - \frac{12150636535}{2} a + \frac{5069473275}{2} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - a - 4\) , \( a^{2} - 3\) , \( 494268 a^{2} - 261626 a - 2100217\) , \( -276978244 a^{2} + 146609177 a + 1176919485\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(494268a^{2}-261626a-2100217\right){x}-276978244a^{2}+146609177a+1176919485$ |
| 242.3-b3 |
242.3-b |
$8$ |
$16$ |
3.3.316.1 |
$3$ |
$[3, 0]$ |
242.3 |
\( 2 \cdot 11^{2} \) |
\( 2^{2} \cdot 11^{6} \) |
$3.96538$ |
$(-a+1), (a^2-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$10.69172574$ |
1.202913127 |
\( \frac{8525185037}{4} a^{2} - \frac{12150636535}{2} a + \frac{5069473275}{2} \) |
\( \bigl[a^{2} + a - 3\) , \( -a + 1\) , \( a\) , \( 10200132836 a^{2} - 5399099430 a - 43341797926\) , \( 820000263652323 a^{2} - 434039735261194 a - 3484296361562003\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(10200132836a^{2}-5399099430a-43341797926\right){x}+820000263652323a^{2}-434039735261194a-3484296361562003$ |
*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.
