| 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 |
| 2916.1-a2 |
2916.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{12} \cdot 3^{8} \) |
$1.13736$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.101978294$ |
$3.305583379$ |
1.556987840 |
\( \frac{109503}{64} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 4\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+4{x}-1$ |
| 13122.1-a2 |
13122.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13122.1 |
\( 2 \cdot 3^{8} \) |
\( 2^{12} \cdot 3^{20} \) |
$1.91280$ |
$(a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cn, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.101978294$ |
$1.101861126$ |
1.348391023 |
\( \frac{109503}{64} \) |
\( \bigl[i\) , \( 1\) , \( 0\) , \( 39\) , \( 19\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+{x}^{2}+39{x}+19$ |
| 26244.2-a2 |
26244.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
26244.2 |
\( 2^{2} \cdot 3^{8} \) |
\( 2^{12} \cdot 3^{20} \) |
$3.00916$ |
$(a), (-a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.101978294$ |
$1.101861126$ |
2.038575609 |
\( \frac{109503}{64} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 39\) , \( -19\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+39{x}-19$ |
| 13122.5-b2 |
13122.5-b |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
13122.5 |
\( 2 \cdot 3^{8} \) |
\( 2^{12} \cdot 3^{20} \) |
$2.70510$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.101978294$ |
$1.101861126$ |
2.860369308 |
\( \frac{109503}{64} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 39\) , \( -19\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+39{x}-19$ |
| 26244.5-a2 |
26244.5-a |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
26244.5 |
\( 2^{2} \cdot 3^{8} \) |
\( 2^{12} \cdot 3^{20} \) |
$3.77218$ |
$(-a), (a-1), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3^{3} \) |
$0.047461481$ |
$1.101861126$ |
6.811700614 |
\( \frac{109503}{64} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 39\) , \( -19\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+39{x}-19$ |
| 1458.1-n2 |
1458.1-n |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{12} \cdot 3^{8} \) |
$1.91280$ |
$(a+1), (a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.101978294$ |
$6.439972360$ |
2.275005083 |
\( \frac{109503}{64} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 3\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+3{x}$ |
| 648.1-f2 |
648.1-f |
$2$ |
$3$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
648.1 |
\( 2^{3} \cdot 3^{4} \) |
\( - 2^{18} \cdot 3^{6} \) |
$2.36579$ |
$(-a^2+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$0.101978294$ |
$28.30652990$ |
1.924434430 |
\( \frac{109503}{64} \) |
\( \bigl[a^{2} + a - 1\) , \( -a^{2} - a + 1\) , \( a\) , \( -8 a^{2} + 2 a + 22\) , \( -3 a^{2} + a + 8\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(-8a^{2}+2a+22\right){x}-3a^{2}+a+8$ |
| 18.1-c1 |
18.1-c |
$2$ |
$3$ |
3.3.1620.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2^{18} \cdot 3^{6} \) |
$5.82248$ |
$(a+2), (a+1)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \) |
$0.096843165$ |
$28.30652990$ |
2.451887866 |
\( \frac{109503}{64} \) |
\( \bigl[a^{2} - 2 a - 7\) , \( -a^{2} + 2 a + 8\) , \( a + 1\) , \( -11489 a^{2} + 15979 a + 115644\) , \( 100088 a^{2} - 139214 a - 1007426\bigr] \) |
${y}^2+\left(a^{2}-2a-7\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+2a+8\right){x}^{2}+\left(-11489a^{2}+15979a+115644\right){x}+100088a^{2}-139214a-1007426$ |
*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.
