| 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 |
| 96.1-b2 |
96.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{9} \cdot 3^{2} \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$17.97674429$ |
1.297359770 |
\( -\frac{164847992914}{3} a + \frac{285525100658}{3} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 9135 a - 15826\) , \( -619924 a + 1073738\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(9135a-15826\right){x}-619924a+1073738$ |
| 96.1-d2 |
96.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{9} \cdot 3^{2} \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.261257214$ |
0.941443865 |
\( -\frac{164847992914}{3} a + \frac{285525100658}{3} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 9137 a - 15823\) , \( 629060 a - 1089563\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(9137a-15823\right){x}+629060a-1089563$ |
| 288.1-a2 |
288.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( - 2^{9} \cdot 3^{8} \) |
$1.27520$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$2.510861184$ |
1.449646380 |
\( -\frac{164847992914}{3} a + \frac{285525100658}{3} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 381758 a - 661224\) , \( 168866036 a - 292484554\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(381758a-661224\right){x}+168866036a-292484554$ |
| 288.1-c2 |
288.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( - 2^{9} \cdot 3^{8} \) |
$1.27520$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.820391757$ |
$7.783091503$ |
1.843243885 |
\( -\frac{164847992914}{3} a + \frac{285525100658}{3} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 381758 a - 661224\) , \( -168866036 a + 292484554\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(381758a-661224\right){x}-168866036a+292484554$ |
| 768.1-a2 |
768.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{21} \cdot 3^{2} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.630628607$ |
1.882887730 |
\( -\frac{164847992914}{3} a + \frac{285525100658}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 36546 a - 63297\) , \( 4995933 a - 8653209\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(36546a-63297\right){x}+4995933a-8653209$ |
| 768.1-p2 |
768.1-p |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{21} \cdot 3^{2} \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.211834002$ |
$8.988372149$ |
2.198599305 |
\( -\frac{164847992914}{3} a + \frac{285525100658}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 36546 a - 63297\) , \( -4995933 a + 8653209\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(36546a-63297\right){x}-4995933a+8653209$ |
| 2304.1-u2 |
2304.1-u |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{21} \cdot 3^{8} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.891545751$ |
2.246784987 |
\( -\frac{164847992914}{3} a + \frac{285525100658}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1527032 a - 2644896\) , \( -1350928288 a + 2339876432\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(1527032a-2644896\right){x}-1350928288a+2339876432$ |
| 2304.1-x2 |
2304.1-x |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{21} \cdot 3^{8} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.255430592$ |
1.449646380 |
\( -\frac{164847992914}{3} a + \frac{285525100658}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 1527032 a - 2644896\) , \( 1350928288 a - 2339876432\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(1527032a-2644896\right){x}+1350928288a-2339876432$ |
| 3072.1-s2 |
3072.1-s |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{27} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.120342961$ |
$4.766150701$ |
2.917314563 |
\( -\frac{164847992914}{3} a + \frac{285525100658}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 272778 a - 472465\) , \( -102151362 a + 176931349\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(272778a-472465\right){x}-102151362a+176931349$ |
| 3072.1-ba2 |
3072.1-ba |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{27} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.739974475$ |
$1.537582179$ |
3.320063175 |
\( -\frac{164847992914}{3} a + \frac{285525100658}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 19584 a - 33920\) , \( 1945592 a - 3369864\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(19584a-33920\right){x}+1945592a-3369864$ |
| 3072.1-be2 |
3072.1-be |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{27} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.537582179$ |
1.775446970 |
\( -\frac{164847992914}{3} a + \frac{285525100658}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 272778 a - 472465\) , \( 102151362 a - 176931349\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(272778a-472465\right){x}+102151362a-176931349$ |
| 3072.1-bk2 |
3072.1-bk |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{27} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.766150701$ |
2.751738390 |
\( -\frac{164847992914}{3} a + \frac{285525100658}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 19584 a - 33920\) , \( -1945592 a + 3369864\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(19584a-33920\right){x}-1945592a+3369864$ |
*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.
