| 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-a5 |
196.2-a |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
196.2 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{20} \) |
$0.57911$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.437708567$ |
0.505422318 |
\( -\frac{14378731676028886375}{3256827195820898} a + \frac{34112602872034890375}{3256827195820898} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 184 a - 415\) , \( 1880 a - 2686\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(184a-415\right){x}+1880a-2686$ |
| 9604.3-c5 |
9604.3-c |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
9604.3 |
\( 2^{2} \cdot 7^{4} \) |
\( 2^{2} \cdot 7^{32} \) |
$1.53219$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$9$ |
\( 2^{4} \) |
$1$ |
$0.062529795$ |
2.599314781 |
\( -\frac{14378731676028886375}{3256827195820898} a + \frac{34112602872034890375}{3256827195820898} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 11270 a + 9040\) , \( -633570 a + 930252\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(11270a+9040\right){x}-633570a+930252$ |
| 12348.2-a6 |
12348.2-a |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12348.2 |
\( 2^{2} \cdot 3^{2} \cdot 7^{3} \) |
\( 2^{2} \cdot 3^{6} \cdot 7^{26} \) |
$1.63154$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{4} \) |
$2.637158682$ |
$0.095515840$ |
2.326864094 |
\( -\frac{14378731676028886375}{3256827195820898} a + \frac{34112602872034890375}{3256827195820898} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( 6498 a - 8288\) , \( -257025 a + 185318\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(6498a-8288\right){x}-257025a+185318$ |
| 12348.3-a6 |
12348.3-a |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12348.3 |
\( 2^{2} \cdot 3^{2} \cdot 7^{3} \) |
\( 2^{2} \cdot 3^{6} \cdot 7^{26} \) |
$1.63154$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{4} \) |
$2.637158682$ |
$0.095515840$ |
2.326864094 |
\( -\frac{14378731676028886375}{3256827195820898} a + \frac{34112602872034890375}{3256827195820898} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( 697 a - 7878\) , \( -47535 a + 249773\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(697a-7878\right){x}-47535a+249773$ |
| 12544.2-k6 |
12544.2-k |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{26} \cdot 7^{20} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{4} \) |
$3.157002788$ |
$0.109427141$ |
3.191239339 |
\( -\frac{14378731676028886375}{3256827195820898} a + \frac{34112602872034890375}{3256827195820898} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 3680 a + 2952\) , \( -120320 a + 171888\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(3680a+2952\right){x}-120320a+171888$ |
| 33124.4-c6 |
33124.4-c |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
33124.4 |
\( 2^{2} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 7^{20} \cdot 13^{6} \) |
$2.08802$ |
$(-3a+1), (3a-2), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.121398514$ |
2.523220734 |
\( -\frac{14378731676028886375}{3256827195820898} a + \frac{34112602872034890375}{3256827195820898} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( 4741 a - 134\) , \( 2953 a - 113338\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(4741a-134\right){x}+2953a-113338$ |
| 33124.6-c6 |
33124.6-c |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
33124.6 |
\( 2^{2} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 7^{20} \cdot 13^{6} \) |
$2.08802$ |
$(-3a+1), (3a-2), (4a-3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$9$ |
\( 2^{3} \) |
$1$ |
$0.121398514$ |
2.523220734 |
\( -\frac{14378731676028886375}{3256827195820898} a + \frac{34112602872034890375}{3256827195820898} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -4926 a + 548\) , \( 128647 a - 74665\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4926a+548\right){x}+128647a-74665$ |
| 87808.2-a6 |
87808.2-a |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87808.2 |
\( 2^{8} \cdot 7^{3} \) |
\( 2^{26} \cdot 7^{26} \) |
$2.66430$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{5} \) |
$3.359079322$ |
$0.041359572$ |
2.566762269 |
\( -\frac{14378731676028886375}{3256827195820898} a + \frac{34112602872034890375}{3256827195820898} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -9545 a - 34653\) , \( -852103 a - 2328103\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-9545a-34653\right){x}-852103a-2328103$ |
| 87808.2-r6 |
87808.2-r |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87808.2 |
\( 2^{8} \cdot 7^{3} \) |
\( 2^{26} \cdot 7^{26} \) |
$2.66430$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$9$ |
\( 2^{5} \) |
$1$ |
$0.041359572$ |
3.438570245 |
\( -\frac{14378731676028886375}{3256827195820898} a + \frac{34112602872034890375}{3256827195820898} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 44198 a - 9545\) , \( 852103 a + 2328103\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(44198a-9545\right){x}+852103a+2328103$ |
| 87808.3-c6 |
87808.3-c |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87808.3 |
\( 2^{8} \cdot 7^{3} \) |
\( 2^{26} \cdot 7^{26} \) |
$2.66430$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{5} \) |
$3.359079322$ |
$0.041359572$ |
2.566762269 |
\( -\frac{14378731676028886375}{3256827195820898} a + \frac{34112602872034890375}{3256827195820898} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -38295 a - 3718\) , \( 3218023 a - 1142126\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-38295a-3718\right){x}+3218023a-1142126$ |
| 87808.3-t6 |
87808.3-t |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87808.3 |
\( 2^{8} \cdot 7^{3} \) |
\( 2^{26} \cdot 7^{26} \) |
$2.66430$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$0.041359572$ |
3.438570245 |
\( -\frac{14378731676028886375}{3256827195820898} a + \frac{34112602872034890375}{3256827195820898} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 42013 a - 38295\) , \( -3218023 a + 1142126\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(42013a-38295\right){x}-3218023a+1142126$ |
| 112896.2-r6 |
112896.2-r |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{26} \cdot 3^{6} \cdot 7^{20} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$9$ |
\( 2^{4} \) |
$1$ |
$0.063177789$ |
2.626251405 |
\( -\frac{14378731676028886375}{3256827195820898} a + \frac{34112602872034890375}{3256827195820898} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -11039 a - 8855\) , \( -690263 a - 195216\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-11039a-8855\right){x}-690263a-195216$ |
| 112896.2-ba6 |
112896.2-ba |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{26} \cdot 3^{6} \cdot 7^{20} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.063177789$ |
2.626251405 |
\( -\frac{14378731676028886375}{3256827195820898} a + \frac{34112602872034890375}{3256827195820898} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 19896 a - 11040\) , \( 670368 a + 206256\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(19896a-11040\right){x}+670368a+206256$ |
| 122500.2-e6 |
122500.2-e |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
122500.2 |
\( 2^{2} \cdot 5^{4} \cdot 7^{2} \) |
\( 2^{2} \cdot 5^{12} \cdot 7^{20} \) |
$2.89556$ |
$(-3a+1), (3a-2), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$9$ |
\( 2^{4} \) |
$1$ |
$0.087541713$ |
3.639040694 |
\( -\frac{14378731676028886375}{3256827195820898} a + \frac{34112602872034890375}{3256827195820898} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 4613 a - 10363\) , \( 229250 a - 340331\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(4613a-10363\right){x}+229250a-340331$ |
*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.
