| 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-a5 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{4} \) |
$0.56231$ |
$(a+1), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$3.939377108$ |
0.437708567 |
\( \frac{128787625}{98} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( -10\) , \( -12\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-10{x}-12$ |
| 4802.1-a5 |
4802.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
4802.1 |
\( 2 \cdot 7^{4} \) |
\( 2^{2} \cdot 7^{16} \) |
$1.48773$ |
$(a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.779379370$ |
$0.562768158$ |
1.754439571 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -515\) , \( -4717\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-515{x}-4717$ |
| 7938.1-b5 |
7938.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
7938.1 |
\( 2 \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{12} \cdot 7^{4} \) |
$1.68693$ |
$(a+1), (3), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$0.350778087$ |
$1.313125702$ |
3.684925782 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -95\) , \( -331\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-95{x}-331$ |
| 12544.1-e5 |
12544.1-e |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12544.1 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{26} \cdot 7^{4} \) |
$1.89137$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.984844277$ |
1.969688554 |
\( \frac{128787625}{98} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 168\) , \( -784 i\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+168{x}-784i$ |
| 19600.1-b5 |
19600.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
19600.1 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{14} \cdot 5^{6} \cdot 7^{4} \) |
$2.11462$ |
$(a+1), (-a-2), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.998673912$ |
$0.880871500$ |
3.518813550 |
\( \frac{128787625}{98} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -168 i - 126\) , \( -1078 i - 196\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-168i-126\right){x}-1078i-196$ |
| 19600.3-b5 |
19600.3-b |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
19600.3 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{14} \cdot 5^{6} \cdot 7^{4} \) |
$2.11462$ |
$(a+1), (2a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.998673912$ |
$0.880871500$ |
3.518813550 |
\( \frac{128787625}{98} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 168 i - 126\) , \( -1078 i + 196\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(168i-126\right){x}-1078i+196$ |
| 28322.1-a5 |
28322.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28322.1 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{2} \cdot 7^{4} \cdot 17^{6} \) |
$2.31846$ |
$(a+1), (a+4), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.955439289$ |
3.821757156 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( -i\) , \( 1\) , \( 84 i + 157\) , \( 637 i - 576\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-i{x}^{2}+\left(84i+157\right){x}+637i-576$ |
| 28322.3-a5 |
28322.3-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28322.3 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{2} \cdot 7^{4} \cdot 17^{6} \) |
$2.31846$ |
$(a+1), (a-4), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.955439289$ |
3.821757156 |
\( \frac{128787625}{98} \) |
\( \bigl[i\) , \( -i\) , \( i\) , \( -84 i + 158\) , \( 637 i + 576\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-i{x}^{2}+\left(-84i+158\right){x}+637i+576$ |
| 50176.1-i5 |
50176.1-i |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50176.1 |
\( 2^{10} \cdot 7^{2} \) |
\( 2^{32} \cdot 7^{4} \) |
$2.67481$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.696390066$ |
1.392780133 |
\( \frac{128787625}{98} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -336 i\) , \( 1568 i - 1568\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}-336i{x}+1568i-1568$ |
| 50176.1-k5 |
50176.1-k |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50176.1 |
\( 2^{10} \cdot 7^{2} \) |
\( 2^{32} \cdot 7^{4} \) |
$2.67481$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.696390066$ |
1.392780133 |
\( \frac{128787625}{98} \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 336 i\) , \( -1568 i - 1568\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+336i{x}-1568i-1568$ |
| 61250.3-e5 |
61250.3-e |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
61250.3 |
\( 2 \cdot 5^{4} \cdot 7^{2} \) |
\( 2^{2} \cdot 5^{12} \cdot 7^{4} \) |
$2.81155$ |
$(a+1), (-a-2), (2a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1.027270605$ |
$0.787875421$ |
6.474890094 |
\( \frac{128787625}{98} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( -262\) , \( -1531\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}-262{x}-1531$ |
*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.
