| 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-a8 |
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 |
\( \frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 55 a - 111\) , \( -406 a + 717\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(55a-111\right){x}-406a+717$ |
| 24.1-b8 |
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 |
\( \frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 53 a - 114\) , \( 460 a - 830\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(53a-114\right){x}+460a-830$ |
| 144.1-a8 |
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 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.197737158$ |
1.211782339 |
\( \frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -211 a - 410\) , \( 2494 a + 4157\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-211a-410\right){x}+2494a+4157$ |
| 144.1-c8 |
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 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.098868579$ |
1.211782339 |
\( \frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 2492 a - 4320\) , \( -117544 a + 203588\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(2492a-4320\right){x}-117544a+203588$ |
| 768.1-e8 |
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 |
\( \frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 218 a - 449\) , \( 3467 a - 6183\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(218a-449\right){x}+3467a-6183$ |
| 768.1-l8 |
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 |
\( \frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 218 a - 449\) , \( -3467 a + 6183\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(218a-449\right){x}-3467a+6183$ |
| 2304.1-q8 |
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 |
$1$ |
\( 2^{2} \) |
$2.786181258$ |
$2.098868579$ |
3.376245242 |
\( \frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 9968 a - 17280\) , \( 940352 a - 1628704\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(9968a-17280\right){x}+940352a-1628704$ |
| 2304.1-bb8 |
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 |
$1$ |
\( 2^{3} \) |
$2.786181258$ |
$1.049434289$ |
3.376245242 |
\( \frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 9968 a - 17280\) , \( -940352 a + 1628704\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(9968a-17280\right){x}-940352a+1628704$ |
| 3072.1-e8 |
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 |
$4$ |
\( 2^{2} \) |
$1$ |
$2.570578528$ |
2.968248410 |
\( \frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 24812 a - 42976\) , \( 3661724 a - 6342292\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(24812a-42976\right){x}+3661724a-6342292$ |
| 3072.1-f8 |
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 |
$1$ |
\( 2 \) |
$3.719487697$ |
$2.570578528$ |
2.760090861 |
\( \frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1770 a - 3105\) , \( 69998 a - 121131\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(1770a-3105\right){x}+69998a-121131$ |
| 3072.1-bt8 |
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 |
$16$ |
\( 2 \) |
$1$ |
$1.285289264$ |
2.968248410 |
\( \frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 1770 a - 3105\) , \( -69998 a + 121131\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(1770a-3105\right){x}-69998a+121131$ |
| 3072.1-cc8 |
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 |
$1$ |
\( 2^{2} \) |
$3.719487697$ |
$1.285289264$ |
2.760090861 |
\( \frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 24812 a - 42976\) , \( -3661724 a + 6342292\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(24812a-42976\right){x}-3661724a+6342292$ |
*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.
