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 |
98.1-a6 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{4} \) |
$0.56231$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.437708567$ |
0.437708567 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( -2730\) , \( 55146\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-2730{x}+55146$ |
4802.1-a6 |
4802.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
4802.1 |
\( 2 \cdot 7^{4} \) |
\( 2^{18} \cdot 7^{16} \) |
$1.48773$ |
$(a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$7.014414334$ |
$0.062529795$ |
1.754439571 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -133795\) , \( 18781197\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-133795{x}+18781197$ |
7938.1-b6 |
7938.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
7938.1 |
\( 2 \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{18} \cdot 3^{12} \cdot 7^{4} \) |
$1.68693$ |
$(a+1), (3), (7)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$3.157002788$ |
$0.145902855$ |
3.684925782 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -24575\) , \( 1488935\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-24575{x}+1488935$ |
12544.1-e6 |
12544.1-e |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12544.1 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{42} \cdot 7^{4} \) |
$1.89137$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{3} \) |
$1$ |
$0.109427141$ |
1.969688554 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 43688\) , \( 3529328 i\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+43688{x}+3529328i$ |
19600.1-b6 |
19600.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
19600.1 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{30} \cdot 5^{6} \cdot 7^{4} \) |
$2.11462$ |
$(a+1), (-a-2), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$8.988065212$ |
$0.097874611$ |
3.518813550 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -43688 i - 32766\) , \( 4852826 i + 882332\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-43688i-32766\right){x}+4852826i+882332$ |
19600.3-b6 |
19600.3-b |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
19600.3 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{30} \cdot 5^{6} \cdot 7^{4} \) |
$2.11462$ |
$(a+1), (2a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$8.988065212$ |
$0.097874611$ |
3.518813550 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 43688 i - 32766\) , \( 4852826 i - 882332\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(43688i-32766\right){x}+4852826i-882332$ |
28322.1-a6 |
28322.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28322.1 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{18} \cdot 7^{4} \cdot 17^{6} \) |
$2.31846$ |
$(a+1), (a+4), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.106159921$ |
3.821757156 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( -i\) , \( 1\) , \( 21844 i + 40957\) , \( -2867579 i + 2591850\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-i{x}^{2}+\left(21844i+40957\right){x}-2867579i+2591850$ |
28322.3-a6 |
28322.3-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28322.3 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{18} \cdot 7^{4} \cdot 17^{6} \) |
$2.31846$ |
$(a+1), (a-4), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.106159921$ |
3.821757156 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[i\) , \( -i\) , \( i\) , \( -21844 i + 40958\) , \( -2867579 i - 2591850\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-i{x}^{2}+\left(-21844i+40958\right){x}-2867579i-2591850$ |
50176.1-i6 |
50176.1-i |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50176.1 |
\( 2^{10} \cdot 7^{2} \) |
\( 2^{48} \cdot 7^{4} \) |
$2.67481$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{3} \) |
$1$ |
$0.077376674$ |
1.392780133 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -87376 i\) , \( -7058656 i + 7058656\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}-87376i{x}-7058656i+7058656$ |
50176.1-k6 |
50176.1-k |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50176.1 |
\( 2^{10} \cdot 7^{2} \) |
\( 2^{48} \cdot 7^{4} \) |
$2.67481$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{3} \) |
$1$ |
$0.077376674$ |
1.392780133 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 87376 i\) , \( 7058656 i + 7058656\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+87376i{x}+7058656i+7058656$ |
61250.3-e6 |
61250.3-e |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
61250.3 |
\( 2 \cdot 5^{4} \cdot 7^{2} \) |
\( 2^{18} \cdot 5^{12} \cdot 7^{4} \) |
$2.81155$ |
$(a+1), (-a-2), (2a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1.027270605$ |
$0.087541713$ |
6.474890094 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( -68262\) , \( 6893219\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}-68262{x}+6893219$ |
*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.