| 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-a1 |
24.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( - 2^{10} \cdot 3 \) |
$0.68514$ |
$(a+1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$18.60223895$ |
0.671250479 |
\( -\frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 1035 a - 1791\) , \( -23450 a + 40617\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(1035a-1791\right){x}-23450a+40617$ |
| 24.1-b1 |
24.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( - 2^{10} \cdot 3 \) |
$0.68514$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1.420877129$ |
0.820343793 |
\( -\frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 1033 a - 1794\) , \( 24484 a - 42410\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(1033a-1794\right){x}+24484a-42410$ |
| 144.1-a1 |
144.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{10} \cdot 3^{7} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.098868579$ |
1.211782339 |
\( -\frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 209 a - 410\) , \( 2494 a - 4159\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(209a-410\right){x}+2494a-4159$ |
| 144.1-c1 |
144.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{10} \cdot 3^{7} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.197737158$ |
1.211782339 |
\( -\frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 43232 a - 74880\) , \( -6451984 a + 11175164\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(43232a-74880\right){x}-6451984a+11175164$ |
| 768.1-e1 |
768.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{22} \cdot 3 \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$0.710438564$ |
1.640687586 |
\( -\frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 4138 a - 7169\) , \( 191739 a - 332103\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(4138a-7169\right){x}+191739a-332103$ |
| 768.1-l1 |
768.1-l |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{22} \cdot 3 \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.079273864$ |
$9.301119475$ |
2.897852395 |
\( -\frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4138 a - 7169\) , \( -191739 a + 332103\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(4138a-7169\right){x}-191739a+332103$ |
| 2304.1-q1 |
2304.1-q |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{22} \cdot 3^{7} \) |
$2.14462$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.786181258$ |
$1.049434289$ |
3.376245242 |
\( -\frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 172928 a - 299520\) , \( 51615872 a - 89401312\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(172928a-299520\right){x}+51615872a-89401312$ |
| 2304.1-bb1 |
2304.1-bb |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{22} \cdot 3^{7} \) |
$2.14462$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.786181258$ |
$2.098868579$ |
3.376245242 |
\( -\frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 172928 a - 299520\) , \( -51615872 a + 89401312\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(172928a-299520\right){x}-51615872a+89401312$ |
| 3072.1-e1 |
3072.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{28} \cdot 3 \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$1.285289264$ |
2.968248410 |
\( -\frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 430252 a - 745216\) , \( 202069724 a - 349995028\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(430252a-745216\right){x}+202069724a-349995028$ |
| 3072.1-f1 |
3072.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{28} \cdot 3 \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.719487697$ |
$1.285289264$ |
2.760090861 |
\( -\frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 30890 a - 53505\) , \( 3879118 a - 6718827\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(30890a-53505\right){x}+3879118a-6718827$ |
| 3072.1-bt1 |
3072.1-bt |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{28} \cdot 3 \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$2.570578528$ |
2.968248410 |
\( -\frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 30890 a - 53505\) , \( -3879118 a + 6718827\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(30890a-53505\right){x}-3879118a+6718827$ |
| 3072.1-cc1 |
3072.1-cc |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{28} \cdot 3 \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.719487697$ |
$2.570578528$ |
2.760090861 |
\( -\frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 430252 a - 745216\) , \( -202069724 a + 349995028\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(430252a-745216\right){x}-202069724a+349995028$ |
*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.
