| 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 |
| 196.2-a3 |
196.2-a |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
196.2 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$0.57911$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/3\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1[2] |
$1$ |
\( 2 \cdot 3^{3} \) |
$1$ |
$2.626251405$ |
0.505422318 |
\( \frac{9938375}{21952} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 4 a - 5\) , \( -6\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(4a-5\right){x}-6$ |
| 9604.3-c3 |
9604.3-c |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
9604.3 |
\( 2^{2} \cdot 7^{4} \) |
\( 2^{12} \cdot 7^{18} \) |
$1.53219$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.375178772$ |
2.599314781 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 220\) , \( 2192\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+220{x}+2192$ |
| 12348.2-a3 |
12348.2-a |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12348.2 |
\( 2^{2} \cdot 3^{2} \cdot 7^{3} \) |
\( 2^{12} \cdot 3^{6} \cdot 7^{12} \) |
$1.63154$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{4} \) |
$0.439526447$ |
$0.573095040$ |
2.326864094 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( 108 a - 68\) , \( -345 a + 638\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(108a-68\right){x}-345a+638$ |
| 12348.3-a3 |
12348.3-a |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12348.3 |
\( 2^{2} \cdot 3^{2} \cdot 7^{3} \) |
\( 2^{12} \cdot 3^{6} \cdot 7^{12} \) |
$1.63154$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{4} \) |
$0.439526447$ |
$0.573095040$ |
2.326864094 |
\( \frac{9938375}{21952} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( 67 a - 108\) , \( 345 a + 293\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(67a-108\right){x}+345a+293$ |
| 12544.2-k3 |
12544.2-k |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{6} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{2} \) |
$2.104668525$ |
$0.656562851$ |
3.191239339 |
\( \frac{9938375}{21952} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 72\) , \( 368\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+72{x}+368$ |
| 33124.4-c3 |
33124.4-c |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
33124.4 |
\( 2^{2} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 7^{6} \cdot 13^{6} \) |
$2.08802$ |
$(-3a+1), (3a-2), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.728391085$ |
2.523220734 |
\( \frac{9938375}{21952} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( 31 a + 36\) , \( -207 a - 98\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(31a+36\right){x}-207a-98$ |
| 33124.6-c3 |
33124.6-c |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
33124.6 |
\( 2^{2} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 7^{6} \cdot 13^{6} \) |
$2.08802$ |
$(-3a+1), (3a-2), (4a-3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.728391085$ |
2.523220734 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -36 a - 32\) , \( 207 a - 305\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-36a-32\right){x}+207a-305$ |
| 87808.2-a3 |
87808.2-a |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87808.2 |
\( 2^{8} \cdot 7^{3} \) |
\( 2^{36} \cdot 7^{12} \) |
$2.66430$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{3} \) |
$2.239386215$ |
$0.248157432$ |
2.566762269 |
\( \frac{9938375}{21952} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 215 a - 573\) , \( -6983 a - 583\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(215a-573\right){x}-6983a-583$ |
| 87808.2-r3 |
87808.2-r |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87808.2 |
\( 2^{8} \cdot 7^{3} \) |
\( 2^{36} \cdot 7^{12} \) |
$2.66430$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.248157432$ |
3.438570245 |
\( \frac{9938375}{21952} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 358 a + 215\) , \( 6983 a + 583\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(358a+215\right){x}+6983a+583$ |
| 87808.3-c3 |
87808.3-c |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87808.3 |
\( 2^{8} \cdot 7^{3} \) |
\( 2^{36} \cdot 7^{12} \) |
$2.66430$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{3} \) |
$2.239386215$ |
$0.248157432$ |
2.566762269 |
\( \frac{9938375}{21952} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -215 a - 358\) , \( 6983 a - 7566\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-215a-358\right){x}+6983a-7566$ |
| 87808.3-t3 |
87808.3-t |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87808.3 |
\( 2^{8} \cdot 7^{3} \) |
\( 2^{36} \cdot 7^{12} \) |
$2.66430$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.248157432$ |
3.438570245 |
\( \frac{9938375}{21952} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 573 a - 215\) , \( -6983 a + 7566\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(573a-215\right){x}-6983a+7566$ |
| 112896.2-r3 |
112896.2-r |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{36} \cdot 3^{6} \cdot 7^{6} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.379066738$ |
2.626251405 |
\( \frac{9938375}{21952} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a - 215\) , \( -2423 a + 1104\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a-215\right){x}-2423a+1104$ |
| 112896.2-ba3 |
112896.2-ba |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{36} \cdot 3^{6} \cdot 7^{6} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.379066738$ |
2.626251405 |
\( \frac{9938375}{21952} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 216 a\) , \( 2208 a - 1104\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+216a{x}+2208a-1104$ |
| 122500.2-e3 |
122500.2-e |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
122500.2 |
\( 2^{2} \cdot 5^{4} \cdot 7^{2} \) |
\( 2^{12} \cdot 5^{12} \cdot 7^{6} \) |
$2.89556$ |
$(-3a+1), (3a-2), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.525250281$ |
3.639040694 |
\( \frac{9938375}{21952} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 113 a - 113\) , \( -831\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(113a-113\right){x}-831$ |
*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.
