| 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 |
| 60.2-b4 |
60.2-b |
$12$ |
$24$ |
\(\Q(\sqrt{-15}) \) |
$2$ |
$[0, 1]$ |
60.2 |
\( 2^{2} \cdot 3 \cdot 5 \) |
\( 2^{36} \cdot 3^{2} \cdot 5^{6} \) |
$0.96321$ |
$(2,a), (2,a+1), (3,a+1), (5,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{6} \cdot 3^{3} \) |
$1$ |
$1.294290140$ |
2.005105663 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 12 a + 42\) , \( -192 a + 447\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+\left(12a+42\right){x}-192a+447$ |
| 2100.1-n5 |
2100.1-n |
$12$ |
$24$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
2100.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
\( 2^{8} \cdot 3^{12} \cdot 5^{12} \cdot 7^{4} \) |
$2.77206$ |
$(-a+2), (-a), (-a+1), (a+3), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{8} \cdot 3^{3} \) |
$0.907803468$ |
$1.384535991$ |
6.582603280 |
\( \frac{21302308926361}{8930250000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -578\) , \( 2756\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-578{x}+2756$ |
| 150.1-b9 |
150.1-b |
$12$ |
$24$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
150.1 |
\( 2 \cdot 3 \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{12} \) |
$1.53203$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{6} \cdot 3^{3} \) |
$1$ |
$5.367489134$ |
3.286902394 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -6671 a - 16341\) , \( 462144 a + 1132017\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-6671a-16341\right){x}+462144a+1132017$ |
| 385.1-A2 |
385.1-A |
$12$ |
$24$ |
3.1.23.1 |
$3$ |
$[1, 1]$ |
385.1 |
\( 5 \cdot 7 \cdot 11 \) |
\( 5^{6} \cdot 7^{4} \cdot 11^{2} \) |
$1.15588$ |
$(a^2+1), (2a^2-a), (a^2+a-2)$ |
0 |
$\Z/2\Z\oplus\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$18.82123964$ |
0.654083292 |
\( \frac{60755460112268}{4539390625} a^{2} - \frac{108198863313337}{4539390625} a + \frac{90250097388021}{4539390625} \) |
\( \bigl[a^{2}\) , \( -a^{2} - a - 1\) , \( a^{2} + 1\) , \( -4 a^{2} + 11 a - 5\) , \( 6 a^{2} - 15 a + 11\bigr] \) |
${y}^2+a^{2}{x}{y}+\left(a^{2}+1\right){y}={x}^{3}+\left(-a^{2}-a-1\right){x}^{2}+\left(-4a^{2}+11a-5\right){x}+6a^{2}-15a+11$ |
*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.
