| 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 |
| 49152.1-e1 |
49152.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{28} \cdot 3 \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.142615817$ |
$2.454726994$ |
3.238715492 |
\( \frac{4736}{3} a - \frac{2560}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -3 a + 8\) , \( 8 a - 3\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a+8\right){x}+8a-3$ |
| 49152.1-h1 |
49152.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{16} \cdot 3 \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.526369266$ |
$4.909453989$ |
2.983960614 |
\( \frac{4736}{3} a - \frac{2560}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -a + 2\) , \( -2 a + 1\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+2\right){x}-2a+1$ |
| 49152.1-q1 |
49152.1-q |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{16} \cdot 3 \) |
$2.30454$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.909453989$ |
2.834474582 |
\( \frac{4736}{3} a - \frac{2560}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -a - 1\) , \( 2 a - 1\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-a-1\right){x}+2a-1$ |
| 49152.1-t1 |
49152.1-t |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49152.1 |
\( 2^{14} \cdot 3 \) |
\( 2^{28} \cdot 3 \) |
$2.30454$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.417557229$ |
$2.454726994$ |
4.018029934 |
\( \frac{4736}{3} a - \frac{2560}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 8 a - 5\) , \( -8 a + 3\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(8a-5\right){x}-8a+3$ |
| 147456.1-e1 |
147456.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
147456.1 |
\( 2^{14} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{7} \) |
$3.03295$ |
$(-2a+1), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.221783341$ |
$2.834474582$ |
5.807120594 |
\( \frac{4736}{3} a - \frac{2560}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 3 a - 6\) , \( 9\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(3a-6\right){x}+9$ |
| 147456.1-f1 |
147456.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
147456.1 |
\( 2^{14} \cdot 3^{2} \) |
\( 2^{28} \cdot 3^{7} \) |
$3.03295$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.148843708$ |
$1.417237291$ |
3.760130219 |
\( \frac{4736}{3} a - \frac{2560}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -23 a + 16\) , \( -14 a + 63\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-23a+16\right){x}-14a+63$ |
| 147456.1-bq1 |
147456.1-bq |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
147456.1 |
\( 2^{14} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{7} \) |
$3.03295$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.834474582$ |
3.272969326 |
\( \frac{4736}{3} a - \frac{2560}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 5 a + 2\) , \( 4 a - 7\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(5a+2\right){x}+4a-7$ |
| 147456.1-br1 |
147456.1-br |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
147456.1 |
\( 2^{14} \cdot 3^{2} \) |
\( 2^{28} \cdot 3^{7} \) |
$3.03295$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.417237291$ |
3.272969326 |
\( \frac{4736}{3} a - \frac{2560}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -23 a + 16\) , \( 14 a - 63\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-23a+16\right){x}+14a-63$ |
*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.
