| 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-a2 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$0.56231$ |
$(a+1), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$7.878754216$ |
0.437708567 |
\( -\frac{15625}{28} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( 0\) , \( 0\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}$ |
| 4802.1-a2 |
4802.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
4802.1 |
\( 2 \cdot 7^{4} \) |
\( 2^{4} \cdot 7^{14} \) |
$1.48773$ |
$(a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.389689685$ |
$1.125536316$ |
1.754439571 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -25\) , \( -111\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-25{x}-111$ |
| 7938.1-b2 |
7938.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
7938.1 |
\( 2 \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 7^{2} \) |
$1.68693$ |
$(a+1), (3), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$0.175389043$ |
$2.626251405$ |
3.684925782 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -5\) , \( -7\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-5{x}-7$ |
| 12544.1-e2 |
12544.1-e |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12544.1 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{28} \cdot 7^{2} \) |
$1.89137$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.969688554$ |
1.969688554 |
\( -\frac{15625}{28} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 8\) , \( -16 i\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+8{x}-16i$ |
| 19600.1-b2 |
19600.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
19600.1 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 5^{6} \cdot 7^{2} \) |
$2.11462$ |
$(a+1), (-a-2), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.499336956$ |
$1.761743000$ |
3.518813550 |
\( -\frac{15625}{28} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -8 i - 6\) , \( -22 i - 4\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-8i-6\right){x}-22i-4$ |
| 19600.3-b2 |
19600.3-b |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
19600.3 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 5^{6} \cdot 7^{2} \) |
$2.11462$ |
$(a+1), (2a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.499336956$ |
$1.761743000$ |
3.518813550 |
\( -\frac{15625}{28} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 8 i - 6\) , \( -22 i + 4\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(8i-6\right){x}-22i+4$ |
| 28322.1-a2 |
28322.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28322.1 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 7^{2} \cdot 17^{6} \) |
$2.31846$ |
$(a+1), (a+4), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.910878578$ |
3.821757156 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( -i\) , \( 1\) , \( 4 i + 7\) , \( 13 i - 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-i{x}^{2}+\left(4i+7\right){x}+13i-12$ |
| 28322.3-a2 |
28322.3-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28322.3 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 7^{2} \cdot 17^{6} \) |
$2.31846$ |
$(a+1), (a-4), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.910878578$ |
3.821757156 |
\( -\frac{15625}{28} \) |
\( \bigl[i\) , \( -i\) , \( i\) , \( -4 i + 8\) , \( 13 i + 12\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-i{x}^{2}+\left(-4i+8\right){x}+13i+12$ |
| 50176.1-i2 |
50176.1-i |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50176.1 |
\( 2^{10} \cdot 7^{2} \) |
\( 2^{34} \cdot 7^{2} \) |
$2.67481$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.392780133$ |
1.392780133 |
\( -\frac{15625}{28} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -16 i\) , \( 32 i - 32\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}-16i{x}+32i-32$ |
| 50176.1-k2 |
50176.1-k |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50176.1 |
\( 2^{10} \cdot 7^{2} \) |
\( 2^{34} \cdot 7^{2} \) |
$2.67481$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.392780133$ |
1.392780133 |
\( -\frac{15625}{28} \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 16 i\) , \( -32 i - 32\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+16i{x}-32i-32$ |
| 61250.3-e2 |
61250.3-e |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
61250.3 |
\( 2 \cdot 5^{4} \cdot 7^{2} \) |
\( 2^{4} \cdot 5^{12} \cdot 7^{2} \) |
$2.81155$ |
$(a+1), (-a-2), (2a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.513635302$ |
$1.575750843$ |
6.474890094 |
\( -\frac{15625}{28} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( -12\) , \( -31\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}-12{x}-31$ |
*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.
