| 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 |
| 3456.3-c2 |
3456.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3456.3 |
\( 2^{7} \cdot 3^{3} \) |
\( 2^{8} \cdot 3^{6} \) |
$1.93788$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.403345156$ |
$4.796561136$ |
2.736036130 |
\( -\frac{48640}{27} a + \frac{74752}{27} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( a - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(a-1\right){x}$ |
| 3456.3-f2 |
3456.3-f |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3456.3 |
\( 2^{7} \cdot 3^{3} \) |
\( 2^{8} \cdot 3^{6} \) |
$1.93788$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.172693842$ |
$4.796561136$ |
3.514334458 |
\( -\frac{48640}{27} a + \frac{74752}{27} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( a - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(a-1\right){x}$ |
| 6912.3-c2 |
6912.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{8} \cdot 3^{12} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.769295863$ |
0.979093942 |
\( -\frac{48640}{27} a + \frac{74752}{27} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -a + 7\) , \( -7 a\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+7\right){x}-7a$ |
| 6912.3-l2 |
6912.3-l |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{8} \cdot 3^{12} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.769295863$ |
2.937281826 |
\( -\frac{48640}{27} a + \frac{74752}{27} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -a + 7\) , \( 7 a\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+7\right){x}+7a$ |
| 10368.3-e2 |
10368.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{18} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.429556282$ |
$1.598853712$ |
3.885114242 |
\( -\frac{48640}{27} a + \frac{74752}{27} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 15 a - 6\) , \( 20 a + 19\bigr] \) |
${y}^2={x}^{3}+\left(15a-6\right){x}+20a+19$ |
| 10368.3-k2 |
10368.3-k |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{18} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.598853712$ |
2.261120604 |
\( -\frac{48640}{27} a + \frac{74752}{27} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 15 a - 6\) , \( -20 a - 19\bigr] \) |
${y}^2={x}^{3}+\left(15a-6\right){x}-20a-19$ |
| 20736.3-g2 |
20736.3-g |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{12} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.769295863$ |
1.958187884 |
\( -\frac{48640}{27} a + \frac{74752}{27} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3 a - 6\) , \( -3 a - 5\bigr] \) |
${y}^2={x}^{3}+\left(-3a-6\right){x}-3a-5$ |
| 20736.3-t2 |
20736.3-t |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{12} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.617377342$ |
$2.769295863$ |
4.835763324 |
\( -\frac{48640}{27} a + \frac{74752}{27} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3 a - 6\) , \( 3 a + 5\bigr] \) |
${y}^2={x}^{3}+\left(-3a-6\right){x}+3a+5$ |
| 27648.3-j2 |
27648.3-j |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{12} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.958187884$ |
1.384647931 |
\( -\frac{48640}{27} a + \frac{74752}{27} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -15\) , \( a + 13\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}-15{x}+a+13$ |
| 27648.3-p2 |
27648.3-p |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{6} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.391680906$ |
2.398280568 |
\( -\frac{48640}{27} a + \frac{74752}{27} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a + 1\) , \( -3 a + 1\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a+1\right){x}-3a+1$ |
| 27648.3-bg2 |
27648.3-bg |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{6} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.429424934$ |
$3.391680906$ |
6.179288852 |
\( -\frac{48640}{27} a + \frac{74752}{27} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4 a + 1\) , \( 3 a - 1\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a+1\right){x}+3a-1$ |
| 27648.3-bm2 |
27648.3-bm |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{12} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.710080596$ |
$1.958187884$ |
5.899269774 |
\( -\frac{48640}{27} a + \frac{74752}{27} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -15\) , \( -a - 13\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}-15{x}-a-13$ |
*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.
