| 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-a2 |
96.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{6} \cdot 3 \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$26.09005771$ |
0.941443865 |
\( -\frac{132636728}{3} a + 76579552 \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 50243 a - 87023\) , \( -8019946 a + 13890954\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(50243a-87023\right){x}-8019946a+13890954$ |
| 96.1-c2 |
96.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{6} \cdot 3 \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8.988372149$ |
1.297359770 |
\( -\frac{132636728}{3} a + 76579552 \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 50243 a - 87026\) , \( 8070189 a - 13977979\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(50243a-87026\right){x}+8070189a-13977979$ |
| 288.1-b2 |
288.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( - 2^{6} \cdot 3^{7} \) |
$1.27520$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.021722368$ |
1.449646380 |
\( -\frac{132636728}{3} a + 76579552 \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 10822 a - 18744\) , \( 809620 a - 1402303\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(10822a-18744\right){x}+809620a-1402303$ |
| 288.1-d2 |
288.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( - 2^{6} \cdot 3^{7} \) |
$1.27520$ |
$(a+1), (a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.410195878$ |
$15.56618300$ |
1.843243885 |
\( -\frac{132636728}{3} a + 76579552 \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 10822 a - 18744\) , \( -809620 a + 1402303\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(10822a-18744\right){x}-809620a+1402303$ |
| 768.1-c2 |
768.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{18} \cdot 3 \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.694672022$ |
$4.494186074$ |
2.198599305 |
\( -\frac{132636728}{3} a + 76579552 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 200974 a - 348097\) , \( 64360541 a - 111475727\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(200974a-348097\right){x}+64360541a-111475727$ |
| 768.1-n2 |
768.1-n |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{18} \cdot 3 \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$13.04502885$ |
1.882887730 |
\( -\frac{132636728}{3} a + 76579552 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 200974 a - 348097\) , \( -64360541 a + 111475727\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(200974a-348097\right){x}-64360541a+111475727$ |
| 2304.1-b2 |
2304.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{18} \cdot 3^{7} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.510861184$ |
1.449646380 |
\( -\frac{132636728}{3} a + 76579552 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 43288 a - 74976\) , \( 6476960 a - 11218424\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(43288a-74976\right){x}+6476960a-11218424$ |
| 2304.1-e2 |
2304.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{18} \cdot 3^{7} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.783091503$ |
2.246784987 |
\( -\frac{132636728}{3} a + 76579552 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 43288 a - 74976\) , \( -6476960 a + 11218424\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(43288a-74976\right){x}-6476960a+11218424$ |
| 3072.1-b2 |
3072.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{24} \cdot 3 \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.060171480$ |
$9.532301402$ |
2.917314563 |
\( -\frac{132636728}{3} a + 76579552 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 107702 a - 186545\) , \( -25356654 a + 43919013\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(107702a-186545\right){x}-25356654a+43919013$ |
| 3072.1-i2 |
3072.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{24} \cdot 3 \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$9.532301402$ |
2.751738390 |
\( -\frac{132636728}{3} a + 76579552 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1500096 a - 2598240\) , \( -1316558104 a + 2280345528\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(1500096a-2598240\right){x}-1316558104a+2280345528$ |
| 3072.1-br2 |
3072.1-br |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{24} \cdot 3 \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$3.075164358$ |
1.775446970 |
\( -\frac{132636728}{3} a + 76579552 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 107702 a - 186545\) , \( 25356654 a - 43919013\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(107702a-186545\right){x}+25356654a-43919013$ |
| 3072.1-cd2 |
3072.1-cd |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{24} \cdot 3 \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.869987237$ |
$3.075164358$ |
3.320063175 |
\( -\frac{132636728}{3} a + 76579552 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 1500096 a - 2598240\) , \( 1316558104 a - 2280345528\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(1500096a-2598240\right){x}+1316558104a-2280345528$ |
*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.
