| 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-a3 |
24.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$0.68514$ |
$(a+1), (a)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$18.60223895$ |
0.671250479 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -38 a + 66\) , \( -168 a + 291\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-38a+66\right){x}-168a+291$ |
| 24.1-b3 |
24.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$0.68514$ |
$(a+1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$11.36701703$ |
0.820343793 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -38 a + 66\) , \( 168 a - 291\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-38a+66\right){x}+168a-291$ |
| 144.1-a3 |
144.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8.395474317$ |
1.211782339 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 8 a + 15\) , \( 25 a + 43\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(8a+15\right){x}+25a+43$ |
| 144.1-c3 |
144.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8.395474317$ |
1.211782339 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -8 a + 15\) , \( -25 a + 43\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-8a+15\right){x}-25a+43$ |
| 768.1-e3 |
768.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$11.36701703$ |
1.640687586 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -520 a + 901\) , \( 10685 a - 18507\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-520a+901\right){x}+10685a-18507$ |
| 768.1-l3 |
768.1-l |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.539636932$ |
$18.60223895$ |
2.897852395 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -520 a + 901\) , \( -10685 a + 18507\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-520a+901\right){x}-10685a+18507$ |
| 2304.1-q3 |
2304.1-q |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$2.14462$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.393090629$ |
$8.395474317$ |
3.376245242 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -21728 a + 37635\) , \( 2826656 a - 4895912\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-21728a+37635\right){x}+2826656a-4895912$ |
| 2304.1-bb3 |
2304.1-bb |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$2.14462$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.393090629$ |
$8.395474317$ |
3.376245242 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -21728 a + 37635\) , \( -2826656 a + 4895912\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-21728a+37635\right){x}-2826656a+4895912$ |
| 3072.1-e3 |
3072.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{14} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$10.28231411$ |
2.968248410 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -54060 a + 93635\) , \( 11124426 a - 19268071\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-54060a+93635\right){x}+11124426a-19268071$ |
| 3072.1-f3 |
3072.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{14} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.464935962$ |
$10.28231411$ |
2.760090861 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -3882 a + 6724\) , \( 217892 a - 377400\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-3882a+6724\right){x}+217892a-377400$ |
| 3072.1-bt3 |
3072.1-bt |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{14} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$10.28231411$ |
2.968248410 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -3882 a + 6724\) , \( -217892 a + 377400\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3882a+6724\right){x}-217892a+377400$ |
| 3072.1-cc3 |
3072.1-cc |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{14} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.464935962$ |
$10.28231411$ |
2.760090861 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -54060 a + 93635\) , \( -11124426 a + 19268071\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-54060a+93635\right){x}-11124426a+19268071$ |
*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.
