| 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 |
| 3528.1-a1 |
3528.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3528.1 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{10} \cdot 3^{4} \cdot 7^{6} \) |
$1.37737$ |
$(a+1), (3), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.748908210$ |
1.748908210 |
\( -\frac{63821054}{3087} a - \frac{1625104}{343} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( 2 i - 27\) , \( -5 i - 63\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(2i-27\right){x}-5i-63$ |
| 3528.1-a2 |
3528.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3528.1 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{11} \cdot 3^{2} \cdot 7^{12} \) |
$1.37737$ |
$(a+1), (3), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$0.874454105$ |
1.748908210 |
\( -\frac{36618425}{352947} a - \frac{212113}{1029} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( 32 i + 3\) , \( -71 i - 201\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(32i+3\right){x}-71i-201$ |
| 3528.1-b1 |
3528.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3528.1 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{8} \) |
$1.37737$ |
$(a+1), (3), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.972356834$ |
1.972356834 |
\( \frac{11696828}{7203} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( -12\) , \( 6 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}-12{x}+6i$ |
| 3528.1-b2 |
3528.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3528.1 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 7^{4} \) |
$1.37737$ |
$(a+1), (3), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3.944713669$ |
1.972356834 |
\( \frac{810448}{441} \) |
\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( 3\) , \( 0\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+3{x}$ |
| 3528.1-b3 |
3528.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3528.1 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
$1.37737$ |
$(a+1), (3), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.944713669$ |
1.972356834 |
\( \frac{2725888}{21} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -7\) , \( -10\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-7{x}-10$ |
| 3528.1-b4 |
3528.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3528.1 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{2} \) |
$1.37737$ |
$(a+1), (3), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.972356834$ |
1.972356834 |
\( \frac{381775972}{567} \) |
\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( 38\) , \( -84 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+38{x}-84i$ |
| 3528.1-c1 |
3528.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3528.1 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{8} \) |
$1.37737$ |
$(a+1), (3), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.390851865$ |
2.086277798 |
\( -\frac{2725888}{64827} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -7\) , \( 52\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-7{x}+52$ |
| 3528.1-c2 |
3528.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3528.1 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{24} \cdot 7^{2} \) |
$1.37737$ |
$(a+1), (3), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.695425932$ |
2.086277798 |
\( \frac{6522128932}{3720087} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 98\) , \( -29 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+98\right){x}-29i$ |
| 3528.1-c3 |
3528.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3528.1 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 7^{4} \) |
$1.37737$ |
$(a+1), (3), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.390851865$ |
2.086277798 |
\( \frac{6940769488}{35721} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 63\) , \( 202 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+63\right){x}+202i$ |
| 3528.1-c4 |
3528.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3528.1 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{2} \) |
$1.37737$ |
$(a+1), (3), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.695425932$ |
2.086277798 |
\( \frac{7080974546692}{189} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 1008\) , \( 12487 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+1008\right){x}+12487i$ |
| 3528.1-d1 |
3528.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3528.1 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{10} \cdot 3^{4} \cdot 7^{6} \) |
$1.37737$ |
$(a+1), (3), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.748908210$ |
1.748908210 |
\( \frac{63821054}{3087} a - \frac{1625104}{343} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( -i - 27\) , \( -22 i - 61\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-i-27\right){x}-22i-61$ |
| 3528.1-d2 |
3528.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3528.1 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{11} \cdot 3^{2} \cdot 7^{12} \) |
$1.37737$ |
$(a+1), (3), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$0.874454105$ |
1.748908210 |
\( \frac{36618425}{352947} a - \frac{212113}{1029} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( -31 i + 3\) , \( 74 i - 169\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-31i+3\right){x}+74i-169$ |
*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.
