| 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 |
| 24.1-a5 |
24.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{8} \cdot 3^{8} \) |
$0.68514$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$9.301119475$ |
0.671250479 |
\( \frac{1556068}{81} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 25 a - 41\) , \( 92 a - 159\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(25a-41\right){x}+92a-159$ |
| 24.1-b5 |
24.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{8} \cdot 3^{8} \) |
$0.68514$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$22.73403407$ |
0.820343793 |
\( \frac{1556068}{81} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 23 a - 44\) , \( -68 a + 116\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(23a-44\right){x}-68a+116$ |
| 144.1-a5 |
144.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{14} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$8.395474317$ |
1.211782339 |
\( \frac{1556068}{81} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a - 20\) , \( -14 a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-20\right){x}-14a-1$ |
| 144.1-c5 |
144.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{14} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$8.395474317$ |
1.211782339 |
\( \frac{1556068}{81} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 1022 a - 1770\) , \( 22034 a - 38164\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(1022a-1770\right){x}+22034a-38164$ |
| 768.1-e5 |
768.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{20} \cdot 3^{8} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$11.36701703$ |
1.640687586 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -98 a - 169\) , \( 637 a + 1105\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-98a-169\right){x}+637a+1105$ |
| 768.1-l5 |
768.1-l |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{20} \cdot 3^{8} \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.539636932$ |
$4.650559737$ |
2.897852395 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -98 a - 169\) , \( -637 a - 1105\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-98a-169\right){x}-637a-1105$ |
| 2304.1-q5 |
2304.1-q |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{14} \) |
$2.14462$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.393090629$ |
$4.197737158$ |
3.376245242 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -72\) , \( -108 a\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}-72{x}-108a$ |
| 2304.1-bb5 |
2304.1-bb |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{14} \) |
$2.14462$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.393090629$ |
$4.197737158$ |
3.376245242 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -72\) , \( 108 a\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}-72{x}+108a$ |
| 3072.1-e5 |
3072.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{26} \cdot 3^{8} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$5.141157056$ |
2.968248410 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 48 a - 96\) , \( -216 a + 360\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(48a-96\right){x}-216a+360$ |
| 3072.1-f5 |
3072.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{26} \cdot 3^{8} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.859743848$ |
$5.141157056$ |
2.760090861 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -48 a - 96\) , \( -216 a - 360\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-48a-96\right){x}-216a-360$ |
| 3072.1-bt5 |
3072.1-bt |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{26} \cdot 3^{8} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$5.141157056$ |
2.968248410 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -48 a - 96\) , \( 216 a + 360\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-48a-96\right){x}+216a+360$ |
| 3072.1-cc5 |
3072.1-cc |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{26} \cdot 3^{8} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.859743848$ |
$5.141157056$ |
2.760090861 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 48 a - 96\) , \( 216 a - 360\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(48a-96\right){x}+216a-360$ |
*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.
