| 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 |
| 96.1-b1 |
96.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{12} \cdot 3 \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8.988372149$ |
1.297359770 |
\( -\frac{166016}{3} a + 95936 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 97256 a - 168452\) , \( 21662226 a - 37520076\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(97256a-168452\right){x}+21662226a-37520076$ |
| 96.1-d1 |
96.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{12} \cdot 3 \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$26.09005771$ |
0.941443865 |
\( -\frac{166016}{3} a + 95936 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 97256 a - 168452\) , \( -21662226 a + 37520076\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(97256a-168452\right){x}-21662226a+37520076$ |
| 288.1-a1 |
288.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{7} \) |
$1.27520$ |
$(a+1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$10.04344473$ |
1.449646380 |
\( -\frac{166016}{3} a + 95936 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 4063804 a - 7038714\) , \( -5839863922 a + 10114941022\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(4063804a-7038714\right){x}-5839863922a+10114941022$ |
| 288.1-c1 |
288.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{7} \) |
$1.27520$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.410195878$ |
$7.783091503$ |
1.843243885 |
\( -\frac{166016}{3} a + 95936 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 4063804 a - 7038714\) , \( 5839863922 a - 10114941022\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(4063804a-7038714\right){x}+5839863922a-10114941022$ |
| 768.1-a1 |
768.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{12} \cdot 3 \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$26.09005771$ |
1.882887730 |
\( -\frac{166016}{3} a + 95936 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1354602 a - 2346237\) , \( -1124664415 a + 1947975909\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(1354602a-2346237\right){x}-1124664415a+1947975909$ |
| 768.1-p1 |
768.1-p |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{12} \cdot 3 \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.694672022$ |
$8.988372149$ |
2.198599305 |
\( -\frac{166016}{3} a + 95936 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 1354602 a - 2346237\) , \( 1124664415 a - 1947975909\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(1354602a-2346237\right){x}+1124664415a-1947975909$ |
| 2304.1-u1 |
2304.1-u |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{7} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.783091503$ |
2.246784987 |
\( -\frac{166016}{3} a + 95936 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 56601488 a - 98036652\) , \( 303715215440 a - 526050184174\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(56601488a-98036652\right){x}+303715215440a-526050184174$ |
| 2304.1-x1 |
2304.1-x |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{7} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$10.04344473$ |
1.449646380 |
\( -\frac{166016}{3} a + 95936 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 56601488 a - 98036652\) , \( -303715215440 a + 526050184174\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(56601488a-98036652\right){x}-303715215440a+526050184174$ |
| 3072.1-s1 |
3072.1-s |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{18} \cdot 3 \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.060171480$ |
$9.532301402$ |
2.917314563 |
\( -\frac{166016}{3} a + 95936 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 10110882 a - 17512561\) , \( 22924388722 a - 39706205999\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(10110882a-17512561\right){x}+22924388722a-39706205999$ |
| 3072.1-ba1 |
3072.1-ba |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{18} \cdot 3 \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.467496809$ |
$12.30065743$ |
3.320063175 |
\( -\frac{166016}{3} a + 95936 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 725928 a - 1257344\) , \( -441742716 a + 765120828\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(725928a-1257344\right){x}-441742716a+765120828$ |
| 3072.1-be1 |
3072.1-be |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{18} \cdot 3 \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$12.30065743$ |
1.775446970 |
\( -\frac{166016}{3} a + 95936 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 10110882 a - 17512561\) , \( -22924388722 a + 39706205999\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(10110882a-17512561\right){x}-22924388722a+39706205999$ |
| 3072.1-bk1 |
3072.1-bk |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{18} \cdot 3 \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$9.532301402$ |
2.751738390 |
\( -\frac{166016}{3} a + 95936 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 725928 a - 1257344\) , \( 441742716 a - 765120828\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(725928a-1257344\right){x}+441742716a-765120828$ |
*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.
