| 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 |
| 2916.1-b2 |
2916.1-b |
$4$ |
$21$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{6} \cdot 3^{8} \) |
$1.13736$ |
$(-2a+1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 7$ |
3B.1.1[2], 7B.2.1 |
$1$ |
\( 3 \) |
$1$ |
$4.084396538$ |
1.572084960 |
\( -\frac{140625}{8} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -5\) , \( 5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-5{x}+5$ |
| 13122.1-c2 |
13122.1-c |
$4$ |
$21$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13122.1 |
\( 2 \cdot 3^{8} \) |
\( 2^{6} \cdot 3^{8} \) |
$1.91280$ |
$(a+1), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 7$ |
3B.1.1, 7B.2.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$4.084396538$ |
2.722931025 |
\( -\frac{140625}{8} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -4\) , \( -5\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-4{x}-5$ |
| 26244.2-l2 |
26244.2-l |
$4$ |
$21$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
26244.2 |
\( 2^{2} \cdot 3^{8} \) |
\( 2^{6} \cdot 3^{8} \) |
$3.00916$ |
$(a), (-a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 7$ |
3B.1.1, 7B.2.1[2] |
$1$ |
\( 3^{2} \) |
$1.679306052$ |
$4.084396538$ |
10.36976045 |
\( -\frac{140625}{8} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -5\) , \( 5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-5{x}+5$ |
| 13122.5-e2 |
13122.5-e |
$4$ |
$21$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
13122.5 |
\( 2 \cdot 3^{8} \) |
\( 2^{6} \cdot 3^{8} \) |
$2.70510$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3, 7$ |
2Cn, 3B.1.1, 7B.2.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$4.084396538$ |
1.925402993 |
\( -\frac{140625}{8} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -5\) , \( 5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-5{x}+5$ |
| 26244.5-b2 |
26244.5-b |
$4$ |
$21$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
26244.5 |
\( 2^{2} \cdot 3^{8} \) |
\( 2^{6} \cdot 3^{8} \) |
$3.77218$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 7$ |
3B.1.1, 7B.2.1 |
$1$ |
\( 3 \) |
$1$ |
$4.084396538$ |
0.820994594 |
\( -\frac{140625}{8} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -5\) , \( 5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-5{x}+5$ |
| 1458.1-p2 |
1458.1-p |
$4$ |
$21$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{6} \cdot 3^{8} \) |
$1.91280$ |
$(a+1), (a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 7$ |
3B.1.1, 7B.2.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.146674927$ |
$25.52176850$ |
4.322510075 |
\( -\frac{140625}{8} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -5\) , \( 5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-5{x}+5$ |
| 8.1-a1 |
8.1-a |
$4$ |
$21$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{9} \) |
$1.13736$ |
$(2)$ |
0 |
$\Z/21\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.1, 7B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$386.8008344$ |
0.292366465 |
\( -\frac{140625}{8} \) |
\( \bigl[a^{2} + a - 1\) , \( -a^{2} + a + 2\) , \( a^{2} - 2\) , \( 13 a^{2} + 2 a - 44\) , \( -22 a^{2} - 3 a + 88\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(13a^{2}+2a-44\right){x}-22a^{2}-3a+88$ |
| 64.1-a2 |
64.1-a |
$4$ |
$21$ |
6.6.820125.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{18} \) |
$114.44414$ |
$(2)$ |
$1$ |
$\Z/21\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.1, 7B.1.1 |
$1$ |
\( 3 \) |
$0.541610385$ |
$149614.8855$ |
3.65221 |
\( -\frac{140625}{8} \) |
\( \bigl[\frac{8}{19} a^{5} + \frac{1}{19} a^{4} - \frac{60}{19} a^{3} - \frac{49}{19} a^{2} - \frac{3}{19} a + \frac{26}{19}\) , \( \frac{4}{19} a^{5} - \frac{9}{19} a^{4} - \frac{30}{19} a^{3} + \frac{61}{19} a^{2} + \frac{27}{19} a - \frac{25}{19}\) , \( \frac{6}{19} a^{5} - \frac{4}{19} a^{4} - \frac{45}{19} a^{3} + \frac{6}{19} a^{2} + \frac{12}{19} a - \frac{9}{19}\) , \( \frac{8}{19} a^{5} + \frac{1}{19} a^{4} - \frac{60}{19} a^{3} - \frac{49}{19} a^{2} - \frac{3}{19} a + \frac{7}{19}\) , \( 0\bigr] \) |
${y}^2+\left(\frac{8}{19}a^{5}+\frac{1}{19}a^{4}-\frac{60}{19}a^{3}-\frac{49}{19}a^{2}-\frac{3}{19}a+\frac{26}{19}\right){x}{y}+\left(\frac{6}{19}a^{5}-\frac{4}{19}a^{4}-\frac{45}{19}a^{3}+\frac{6}{19}a^{2}+\frac{12}{19}a-\frac{9}{19}\right){y}={x}^{3}+\left(\frac{4}{19}a^{5}-\frac{9}{19}a^{4}-\frac{30}{19}a^{3}+\frac{61}{19}a^{2}+\frac{27}{19}a-\frac{25}{19}\right){x}^{2}+\left(\frac{8}{19}a^{5}+\frac{1}{19}a^{4}-\frac{60}{19}a^{3}-\frac{49}{19}a^{2}-\frac{3}{19}a+\frac{7}{19}\right){x}$ |
| 8.1-b2 |
8.1-b |
$4$ |
$21$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{18} \) |
$119.27013$ |
$(-a^4-a^3+3a^2+2a-1)$ |
$1$ |
$\Z/21\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.1, 7B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.146674927$ |
$149614.8855$ |
1.59609 |
\( -\frac{140625}{8} \) |
\( \bigl[a^{4} - 5 a^{2} + 4\) , \( -a^{4} + 6 a^{2} - 7\) , \( a^{2} - 2\) , \( a^{4} - 8 a^{2} + 9\) , \( 2 a^{2} - 3\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+4\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{4}+6a^{2}-7\right){x}^{2}+\left(a^{4}-8a^{2}+9\right){x}+2a^{2}-3$ |
| 64.1-b2 |
64.1-b |
$4$ |
$21$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{18} \) |
$143.67185$ |
$(2)$ |
$1$ |
$\Z/21\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.1, 7B.1.1 |
$1$ |
\( 3 \) |
$0.755652443$ |
$149614.8855$ |
4.05894 |
\( -\frac{140625}{8} \) |
\( \bigl[a^{5} - 6 a^{3} - a^{2} + 5 a\) , \( a^{5} - a^{4} - 6 a^{3} + 4 a^{2} + 6 a - 3\) , \( a^{4} - 5 a^{2} - a + 2\) , \( -a^{5} + 3 a^{4} + 6 a^{3} - 14 a^{2} - 8 a + 5\) , \( -2 a^{4} + 10 a^{2} + 2 a - 3\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}-a^{2}+5a\right){x}{y}+\left(a^{4}-5a^{2}-a+2\right){y}={x}^{3}+\left(a^{5}-a^{4}-6a^{3}+4a^{2}+6a-3\right){x}^{2}+\left(-a^{5}+3a^{4}+6a^{3}-14a^{2}-8a+5\right){x}-2a^{4}+10a^{2}+2a-3$ |
| 64.1-d2 |
64.1-d |
$4$ |
$21$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{18} \) |
$149.39235$ |
$(2)$ |
$1$ |
$\Z/21\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.1, 7B.1.1 |
$1$ |
\( 3 \) |
$0.408506482$ |
$149614.8855$ |
2.11024 |
\( -\frac{140625}{8} \) |
\( \bigl[a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} + 2 a - 1\) , \( a^{5} - 3 a^{4} - 4 a^{3} + 11 a^{2} + 6 a - 6\) , \( a^{3} - 2 a^{2} - 2 a + 3\) , \( -1\) , \( -4 a^{5} + 12 a^{4} + 14 a^{3} - 40 a^{2} - 20 a + 21\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-2a^{3}+7a^{2}+2a-1\right){x}{y}+\left(a^{3}-2a^{2}-2a+3\right){y}={x}^{3}+\left(a^{5}-3a^{4}-4a^{3}+11a^{2}+6a-6\right){x}^{2}-{x}-4a^{5}+12a^{4}+14a^{3}-40a^{2}-20a+21$ |
| 64.1-g2 |
64.1-g |
$4$ |
$21$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{18} \) |
$156.24874$ |
$(2a^5-6a^4-5a^3+12a^2+a-3), (-a^5+3a^4+3a^3-6a^2-2a+1)$ |
0 |
$\Z/21\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.1, 7B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$149614.8855$ |
2.46954 |
\( -\frac{140625}{8} \) |
\( \bigl[a^{5} - 4 a^{4} + 9 a^{2} - 2 a - 3\) , \( -a^{5} + 5 a^{4} - 3 a^{3} - 11 a^{2} + 6 a + 3\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 4 a + 1\) , \( a^{5} - 7 a^{4} + 9 a^{3} + 15 a^{2} - 14 a - 7\) , \( 2 a^{4} - 6 a^{3} - 4 a^{2} + 8 a + 3\bigr] \) |
${y}^2+\left(a^{5}-4a^{4}+9a^{2}-2a-3\right){x}{y}+\left(a^{4}-3a^{3}-2a^{2}+4a+1\right){y}={x}^{3}+\left(-a^{5}+5a^{4}-3a^{3}-11a^{2}+6a+3\right){x}^{2}+\left(a^{5}-7a^{4}+9a^{3}+15a^{2}-14a-7\right){x}+2a^{4}-6a^{3}-4a^{2}+8a+3$ |
*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.
