| 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 |
| 1536.1-d1 |
1536.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1536.1 |
\( 2^{9} \cdot 3 \) |
\( 2^{20} \cdot 3^{12} \) |
$1.93788$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.905995327$ |
0.838888592 |
\( -\frac{219488}{729} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 12 a - 24\) , \( -108 a + 180\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(12a-24\right){x}-108a+180$ |
| 1536.1-g1 |
1536.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1536.1 |
\( 2^{9} \cdot 3 \) |
\( 2^{20} \cdot 3^{12} \) |
$1.93788$ |
$(a+1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$2.905995327$ |
2.516665776 |
\( -\frac{219488}{729} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -12 a - 24\) , \( -108 a - 180\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-12a-24\right){x}-108a-180$ |
| 1536.1-r1 |
1536.1-r |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1536.1 |
\( 2^{9} \cdot 3 \) |
\( 2^{20} \cdot 3^{12} \) |
$1.93788$ |
$(a+1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$2.905995327$ |
2.516665776 |
\( -\frac{219488}{729} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 12 a - 24\) , \( 108 a - 180\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(12a-24\right){x}+108a-180$ |
| 1536.1-u1 |
1536.1-u |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1536.1 |
\( 2^{9} \cdot 3 \) |
\( 2^{20} \cdot 3^{12} \) |
$1.93788$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.905995327$ |
0.838888592 |
\( -\frac{219488}{729} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -12 a - 24\) , \( 108 a + 180\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-12a-24\right){x}+108a+180$ |
| 3072.1-l1 |
3072.1-l |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{14} \cdot 3^{12} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.917567739$ |
2.214216501 |
\( -\frac{219488}{729} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -26 a - 43\) , \( -245 a - 425\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-26a-43\right){x}-245a-425$ |
| 3072.1-n1 |
3072.1-n |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{14} \cdot 3^{12} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.917567739$ |
1.660662376 |
\( -\frac{219488}{729} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -6\) , \( -18\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-6{x}-18$ |
| 3072.1-bj1 |
3072.1-bj |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{14} \cdot 3^{12} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.327571650$ |
$8.807833659$ |
3.375487085 |
\( -\frac{219488}{729} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -6\) , \( 18\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-6{x}+18$ |
| 3072.1-bw1 |
3072.1-bw |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{14} \cdot 3^{12} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.135844784$ |
$8.807833659$ |
4.144791566 |
\( -\frac{219488}{729} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -26 a - 43\) , \( 245 a + 425\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-26a-43\right){x}+245a+425$ |
| 4608.1-d1 |
4608.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{18} \) |
$2.55039$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.595783034$ |
2.076026302 |
\( -\frac{219488}{729} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -38 a - 75\) , \( 503 a + 898\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-38a-75\right){x}+503a+898$ |
| 4608.1-l1 |
4608.1-l |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{18} \) |
$2.55039$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.595783034$ |
2.076026302 |
\( -\frac{219488}{729} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 38 a - 75\) , \( -503 a + 898\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(38a-75\right){x}-503a+898$ |
| 4608.1-x1 |
4608.1-x |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{18} \) |
$2.55039$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$2.230598773$ |
$0.782843751$ |
4.032699974 |
\( -\frac{219488}{729} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 38 a - 75\) , \( 503 a - 898\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(38a-75\right){x}+503a-898$ |
| 4608.1-z1 |
4608.1-z |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{18} \) |
$2.55039$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$2.230598773$ |
$0.782843751$ |
4.032699974 |
\( -\frac{219488}{729} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -38 a - 75\) , \( -503 a - 898\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-38a-75\right){x}-503a-898$ |
*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.
