| 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 |
| 2.1-b4 |
2.1-b |
$4$ |
$6$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{12} \) |
$2.71558$ |
$(a^2-6)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1.100857932$ |
$125.9459139$ |
0.853516891 |
\( \frac{2615577}{4096} a^{2} - \frac{11083745}{4096} a + \frac{12352857}{4096} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} + 5\) , \( 0\) , \( -11 a^{2} + 29 a - 3\) , \( 37 a^{2} - 146 a + 133\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-11a^{2}+29a-3\right){x}+37a^{2}-146a+133$ |
| 16.3-d1 |
16.3-d |
$4$ |
$6$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{24} \) |
$3.84041$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$41.38474842$ |
1.528580560 |
\( \frac{2615577}{4096} a^{2} - \frac{11083745}{4096} a + \frac{12352857}{4096} \) |
\( \bigl[a\) , \( a - 1\) , \( a^{2} - 4\) , \( 21 a^{2} + 31 a - 64\) , \( 260 a^{2} + 395 a - 828\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(21a^{2}+31a-64\right){x}+260a^{2}+395a-828$ |
| 50.2-e3 |
50.2-e |
$4$ |
$6$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
50.2 |
\( 2 \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{6} \) |
$4.64357$ |
$(a^2-6), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.443882723$ |
$47.08646616$ |
2.315973615 |
\( \frac{2615577}{4096} a^{2} - \frac{11083745}{4096} a + \frac{12352857}{4096} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a^{2} - 4\) , \( 117805 a^{2} + 178851 a - 374248\) , \( 99784955 a^{2} + 151493389 a - 317004232\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(117805a^{2}+178851a-374248\right){x}+99784955a^{2}+151493389a-317004232$ |
| 64.4-c2 |
64.4-c |
$4$ |
$6$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{30} \) |
$4.83861$ |
$(a^2-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.749280959$ |
$40.27214784$ |
3.343634184 |
\( \frac{2615577}{4096} a^{2} - \frac{11083745}{4096} a + \frac{12352857}{4096} \) |
\( \bigl[a^{2} + a - 4\) , \( a^{2} - 4\) , \( 0\) , \( -55 a^{2} + 219 a - 180\) , \( 659 a^{2} - 2420 a + 1936\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-55a^{2}+219a-180\right){x}+659a^{2}-2420a+1936$ |
| 64.4-l4 |
64.4-l |
$4$ |
$6$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{30} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$26.46616559$ |
0.977550130 |
\( \frac{2615577}{4096} a^{2} - \frac{11083745}{4096} a + \frac{12352857}{4096} \) |
\( \bigl[a^{2} - 4\) , \( -a + 1\) , \( 0\) , \( -5 a^{2} + 13 a - 1\) , \( -25 a^{2} + 84 a - 53\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5a^{2}+13a-1\right){x}-25a^{2}+84a-53$ |
| 98.2-e1 |
98.2-e |
$4$ |
$6$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$5.19471$ |
$(a^2-6), (a^2+2a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.143229722$ |
$31.28392925$ |
5.958061197 |
\( \frac{2615577}{4096} a^{2} - \frac{11083745}{4096} a + \frac{12352857}{4096} \) |
\( \bigl[1\) , \( -a - 1\) , \( a^{2} - 5\) , \( 47187 a^{2} + 71640 a - 149905\) , \( 25248708 a^{2} + 38332555 a - 80211967\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(47187a^{2}+71640a-149905\right){x}+25248708a^{2}+38332555a-80211967$ |
*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.
