| 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 |
| 192.1-a4 |
192.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$1.15227$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$10.97780010$ |
1.584508961 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -18 a - 29\) , \( -47 a - 81\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-18a-29\right){x}-47a-81$ |
| 192.1-b4 |
192.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$1.15227$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.620169672$ |
$32.06898949$ |
1.435308265 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -18 a - 29\) , \( 47 a + 81\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-18a-29\right){x}+47a+81$ |
| 576.1-a4 |
576.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{8} \) |
$1.51647$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$10.83277367$ |
1.563576199 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -12\) , \( -6 a\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}-12{x}-6a$ |
| 576.1-b4 |
576.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{8} \) |
$1.51647$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$10.83277367$ |
1.563576199 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -12\) , \( 6 a\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}-12{x}+6a$ |
| 768.1-g4 |
768.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$32.06898949$ |
2.314379964 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 242 a - 419\) , \( -2437 a + 4221\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(242a-419\right){x}-2437a+4221$ |
| 768.1-j4 |
768.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.351603734$ |
$10.97780010$ |
2.141628230 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 242 a - 419\) , \( 2437 a - 4221\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(242a-419\right){x}+2437a-4221$ |
| 2304.1-n4 |
2304.1-n |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{8} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$10.83277367$ |
1.563576199 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 10140 a - 17562\) , \( -723720 a + 1253520\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(10140a-17562\right){x}-723720a+1253520$ |
| 2304.1-bd4 |
2304.1-bd |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{8} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$10.83277367$ |
1.563576199 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 52 a - 90\) , \( 296 a - 512\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(52a-90\right){x}+296a-512$ |
| 3072.1-t4 |
3072.1-t |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{18} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$13.26738399$ |
1.914981930 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 1812 a - 3136\) , \( 54640 a - 94640\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(1812a-3136\right){x}+54640a-94640$ |
| 3072.1-z4 |
3072.1-z |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{18} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$13.26738399$ |
1.914981930 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 130 a - 225\) , \( -1086 a + 1881\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(130a-225\right){x}-1086a+1881$ |
| 3072.1-bd4 |
3072.1-bd |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{18} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.061875302$ |
$13.26738399$ |
4.066944035 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 8 a - 16\) , \( -12 a + 20\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(8a-16\right){x}-12a+20$ |
| 3072.1-bl4 |
3072.1-bl |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{18} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.061875302$ |
$13.26738399$ |
4.066944035 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 130 a - 225\) , \( 1086 a - 1881\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(130a-225\right){x}+1086a-1881$ |
*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.
