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 |
171.1-a1 |
171.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{9} \cdot 19^{3} \) |
$0.55969$ |
$(-2a+1), (-5a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.713137527$ |
0.522143560 |
\( \frac{29840721}{6859} a - \frac{35267232}{6859} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -5 a - 5\) , \( 9 a + 3\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-5a-5\right){x}+9a+3$ |
3249.1-a1 |
3249.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3249.1 |
\( 3^{2} \cdot 19^{2} \) |
\( 3^{3} \cdot 19^{9} \) |
$1.16852$ |
$(-2a+1), (-5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1.078091533$ |
1.244872874 |
\( \frac{29840721}{6859} a - \frac{35267232}{6859} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -17 a + 56\) , \( -156 a + 42\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-17a+56\right){x}-156a+42$ |
8379.1-a1 |
8379.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
8379.1 |
\( 3^{2} \cdot 7^{2} \cdot 19 \) |
\( 3^{3} \cdot 7^{6} \cdot 19^{3} \) |
$1.48080$ |
$(-2a+1), (-3a+1), (-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.190951457$ |
$1.776165441$ |
2.349778965 |
\( \frac{29840721}{6859} a - \frac{35267232}{6859} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -17 a + 19\) , \( 11 a + 34\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-17a+19\right){x}+11a+34$ |
8379.5-d1 |
8379.5-d |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
8379.5 |
\( 3^{2} \cdot 7^{2} \cdot 19 \) |
\( 3^{3} \cdot 7^{6} \cdot 19^{3} \) |
$1.48080$ |
$(-2a+1), (3a-2), (-5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1.776165441$ |
2.050939191 |
\( \frac{29840721}{6859} a - \frac{35267232}{6859} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 19 a - 17\) , \( 46 a - 16\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(19a-17\right){x}+46a-16$ |
28899.1-d1 |
28899.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.1 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{9} \cdot 13^{6} \cdot 19^{3} \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.870555393$ |
$0.752488959$ |
3.025700258 |
\( \frac{29840721}{6859} a - \frac{35267232}{6859} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -6 a + 106\) , \( 525 a - 306\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-6a+106\right){x}+525a-306$ |
28899.5-c1 |
28899.5-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.5 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{9} \cdot 13^{6} \cdot 19^{3} \) |
$2.01799$ |
$(-2a+1), (4a-3), (-5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.752488959$ |
2.606698220 |
\( \frac{29840721}{6859} a - \frac{35267232}{6859} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -3 a - 102\) , \( 54 a + 409\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-3a-102\right){x}+54a+409$ |
43776.1-b1 |
43776.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
43776.1 |
\( 2^{8} \cdot 3^{2} \cdot 19 \) |
\( 2^{24} \cdot 3^{3} \cdot 19^{3} \) |
$2.23876$ |
$(-2a+1), (-5a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.178921751$ |
$1.174823011$ |
2.912635915 |
\( \frac{29840721}{6859} a - \frac{35267232}{6859} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -48 a + 24\) , \( 112 a - 160\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-48a+24\right){x}+112a-160$ |
43776.1-o1 |
43776.1-o |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
43776.1 |
\( 2^{8} \cdot 3^{2} \cdot 19 \) |
\( 2^{24} \cdot 3^{9} \cdot 19^{3} \) |
$2.23876$ |
$(-2a+1), (-5a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1.195060975$ |
$0.678284381$ |
3.743960357 |
\( \frac{29840721}{6859} a - \frac{35267232}{6859} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -75 a + 147\) , \( -552 a - 118\bigr] \) |
${y}^2={x}^{3}+\left(-75a+147\right){x}-552a-118$ |
43776.1-q1 |
43776.1-q |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
43776.1 |
\( 2^{8} \cdot 3^{2} \cdot 19 \) |
\( 2^{24} \cdot 3^{3} \cdot 19^{3} \) |
$2.23876$ |
$(-2a+1), (-5a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$1.174823011$ |
2.713137527 |
\( \frac{29840721}{6859} a - \frac{35267232}{6859} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 25 a + 25\) , \( -63 a + 136\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(25a+25\right){x}-63a+136$ |
61731.3-c1 |
61731.3-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
61731.3 |
\( 3^{2} \cdot 19^{3} \) |
\( 3^{3} \cdot 19^{9} \) |
$2.43964$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1.078091533$ |
1.244872874 |
\( \frac{29840721}{6859} a - \frac{35267232}{6859} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -16 a - 40\) , \( -81 a - 75\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-16a-40\right){x}-81a-75$ |
106875.1-a1 |
106875.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
106875.1 |
\( 3^{2} \cdot 5^{4} \cdot 19 \) |
\( 3^{9} \cdot 5^{12} \cdot 19^{3} \) |
$2.79845$ |
$(-2a+1), (-5a+3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.542627505$ |
1.879716818 |
\( \frac{29840721}{6859} a - \frac{35267232}{6859} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -113 a - 117\) , \( 1106 a + 260\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-113a-117\right){x}+1106a+260$ |
*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.