| 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-b4 |
96.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$17.97674429$ |
1.297359770 |
\( \frac{9856}{3} a + \frac{22336}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2720 a - 4711\) , \( -10125 a + 17537\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(2720a-4711\right){x}-10125a+17537$ |
| 96.1-d4 |
96.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$26.09005771$ |
0.941443865 |
\( \frac{9856}{3} a + \frac{22336}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2720 a - 4711\) , \( 10125 a - 17537\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(2720a-4711\right){x}+10125a-17537$ |
| 288.1-a4 |
288.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{8} \) |
$1.27520$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$10.04344473$ |
1.449646380 |
\( \frac{9856}{3} a + \frac{22336}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 113682 a - 196902\) , \( 3469554 a - 6009444\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(113682a-196902\right){x}+3469554a-6009444$ |
| 288.1-c4 |
288.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{8} \) |
$1.27520$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.205097939$ |
$15.56618300$ |
1.843243885 |
\( \frac{9856}{3} a + \frac{22336}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 113682 a - 196902\) , \( -3469554 a + 6009444\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(113682a-196902\right){x}-3469554a+6009444$ |
| 768.1-a4 |
768.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$26.09005771$ |
1.882887730 |
\( \frac{9856}{3} a + \frac{22336}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 37894 a - 65634\) , \( 667716 a - 1156518\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(37894a-65634\right){x}+667716a-1156518$ |
| 768.1-p4 |
768.1-p |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.847336011$ |
$17.97674429$ |
2.198599305 |
\( \frac{9856}{3} a + \frac{22336}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 37894 a - 65634\) , \( -667716 a + 1156518\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(37894a-65634\right){x}-667716a+1156518$ |
| 2304.1-u4 |
2304.1-u |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{8} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$15.56618300$ |
2.246784987 |
\( \frac{9856}{3} a + \frac{22336}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1583386 a - 2742504\) , \( -176024176 a + 304882816\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(1583386a-2742504\right){x}-176024176a+304882816$ |
| 2304.1-x4 |
2304.1-x |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{8} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$10.04344473$ |
1.449646380 |
\( \frac{9856}{3} a + \frac{22336}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 1583386 a - 2742504\) , \( 176024176 a - 304882816\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(1583386a-2742504\right){x}+176024176a-304882816$ |
| 3072.1-s4 |
3072.1-s |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{18} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.530085740$ |
$19.06460280$ |
2.917314563 |
\( \frac{9856}{3} a + \frac{22336}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 282844 a - 489900\) , \( -13616268 a + 23584068\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(282844a-489900\right){x}-13616268a+23584068$ |
| 3072.1-ba4 |
3072.1-ba |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{18} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.934993618$ |
$12.30065743$ |
3.320063175 |
\( \frac{9856}{3} a + \frac{22336}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 20308 a - 35172\) , \( 261948 a - 453708\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(20308a-35172\right){x}+261948a-453708$ |
| 3072.1-be4 |
3072.1-be |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{18} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$12.30065743$ |
1.775446970 |
\( \frac{9856}{3} a + \frac{22336}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 282844 a - 489900\) , \( 13616268 a - 23584068\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(282844a-489900\right){x}+13616268a-23584068$ |
| 3072.1-bk4 |
3072.1-bk |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{18} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$19.06460280$ |
2.751738390 |
\( \frac{9856}{3} a + \frac{22336}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 20308 a - 35172\) , \( -261948 a + 453708\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(20308a-35172\right){x}-261948a+453708$ |
*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.
