| 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-c1 |
3456.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3456.3 |
\( 2^{7} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{9} \) |
$1.93788$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.201672578$ |
$2.398280568$ |
2.736036130 |
\( \frac{335248}{729} a + \frac{350000}{729} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a + 4\) , \( -8 a - 4\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a+4\right){x}-8a-4$ |
| 3456.3-f1 |
3456.3-f |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3456.3 |
\( 2^{7} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{9} \) |
$1.93788$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.086346921$ |
$2.398280568$ |
3.514334458 |
\( \frac{335248}{729} a + \frac{350000}{729} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4 a + 4\) , \( 8 a + 4\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a+4\right){x}+8a+4$ |
| 6912.3-c1 |
6912.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{15} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.384647931$ |
0.979093942 |
\( \frac{335248}{729} a + \frac{350000}{729} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -6 a - 18\) , \( -26 a - 14\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a-18\right){x}-26a-14$ |
| 6912.3-l1 |
6912.3-l |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{15} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.384647931$ |
2.937281826 |
\( \frac{335248}{729} a + \frac{350000}{729} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -6 a - 18\) , \( 26 a + 14\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-6a-18\right){x}+26a+14$ |
| 10368.3-e1 |
10368.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{21} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.859112564$ |
$0.799426856$ |
3.885114242 |
\( \frac{335248}{729} a + \frac{350000}{729} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -30 a + 39\) , \( 146 a + 82\bigr] \) |
${y}^2={x}^{3}+\left(-30a+39\right){x}+146a+82$ |
| 10368.3-k1 |
10368.3-k |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10368.3 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{21} \) |
$2.55039$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.799426856$ |
2.261120604 |
\( \frac{335248}{729} a + \frac{350000}{729} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -30 a + 39\) , \( -146 a - 82\bigr] \) |
${y}^2={x}^{3}+\left(-30a+39\right){x}-146a-82$ |
| 20736.3-g1 |
20736.3-g |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{15} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.384647931$ |
1.958187884 |
\( \frac{335248}{729} a + \frac{350000}{729} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 12 a + 9\) , \( -24 a - 26\bigr] \) |
${y}^2={x}^{3}+\left(12a+9\right){x}-24a-26$ |
| 20736.3-t1 |
20736.3-t |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{15} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.234754684$ |
$1.384647931$ |
4.835763324 |
\( \frac{335248}{729} a + \frac{350000}{729} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 12 a + 9\) , \( 24 a + 26\bigr] \) |
${y}^2={x}^{3}+\left(12a+9\right){x}+24a+26$ |
| 27648.3-j1 |
27648.3-j |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{22} \cdot 3^{15} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.979093942$ |
1.384647931 |
\( \frac{335248}{729} a + \frac{350000}{729} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 10 a + 35\) , \( -17 a + 139\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(10a+35\right){x}-17a+139$ |
| 27648.3-p1 |
27648.3-p |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{22} \cdot 3^{9} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.695840453$ |
2.398280568 |
\( \frac{335248}{729} a + \frac{350000}{729} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 6 a - 9\) , \( -a + 23\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(6a-9\right){x}-a+23$ |
| 27648.3-bg1 |
27648.3-bg |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{22} \cdot 3^{9} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.214712467$ |
$1.695840453$ |
6.179288852 |
\( \frac{335248}{729} a + \frac{350000}{729} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 6 a - 9\) , \( a - 23\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(6a-9\right){x}+a-23$ |
| 27648.3-bm1 |
27648.3-bm |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{22} \cdot 3^{15} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.355040298$ |
$0.979093942$ |
5.899269774 |
\( \frac{335248}{729} a + \frac{350000}{729} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 10 a + 35\) , \( 17 a - 139\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(10a+35\right){x}+17a-139$ |
*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.
