| 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 |
| 1300.4-a4 |
1300.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1300.4 |
\( 2^{2} \cdot 5^{2} \cdot 13 \) |
\( 2^{4} \cdot 5^{8} \cdot 13^{2} \) |
$1.07314$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$2.384403914$ |
1.192201957 |
\( -\frac{4789923264}{2640625} a + \frac{673064048}{2640625} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( -4 i + 7\) , \( -5 i - 10\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+\left(-4i+7\right){x}-5i-10$ |
| 26000.4-j4 |
26000.4-j |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{4} \cdot 5^{14} \cdot 13^{2} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1.876277569$ |
$1.066337847$ |
4.001491570 |
\( -\frac{4789923264}{2640625} a + \frac{673064048}{2640625} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -16 i - 37\) , \( 35 i + 120\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-16i-37\right){x}+35i+120$ |
| 26000.6-b4 |
26000.6-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.6 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{4} \cdot 5^{14} \cdot 13^{2} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1.673310095$ |
$1.066337847$ |
3.568627771 |
\( -\frac{4789923264}{2640625} a + \frac{673064048}{2640625} \) |
\( \bigl[i + 1\) , \( -1\) , \( 0\) , \( 40 i - 5\) , \( -75 i - 100\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-{x}^{2}+\left(40i-5\right){x}-75i-100$ |
| 32500.6-c4 |
32500.6-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
32500.6 |
\( 2^{2} \cdot 5^{4} \cdot 13 \) |
\( 2^{4} \cdot 5^{20} \cdot 13^{2} \) |
$2.39960$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.476880782$ |
0.953761565 |
\( -\frac{4789923264}{2640625} a + \frac{673064048}{2640625} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -101 i + 177\) , \( -449 i - 1150\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-101i+177\right){x}-449i-1150$ |
| 67600.6-i4 |
67600.6-i |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.6 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 5^{8} \cdot 13^{8} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.166562474$ |
$0.661314659$ |
4.628789192 |
\( -\frac{4789923264}{2640625} a + \frac{673064048}{2640625} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( 64 i + 83\) , \( 415 i - 320\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(64i+83\right){x}+415i-320$ |
| 83200.4-g4 |
83200.4-g |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
83200.4 |
\( 2^{8} \cdot 5^{2} \cdot 13 \) |
\( 2^{16} \cdot 5^{8} \cdot 13^{2} \) |
$3.03528$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.192201957$ |
2.384403914 |
\( -\frac{4789923264}{2640625} a + \frac{673064048}{2640625} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( -16 i + 28\) , \( 40 i + 80\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+\left(-16i+28\right){x}+40i+80$ |
| 84500.6-b4 |
84500.6-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
84500.6 |
\( 2^{2} \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{4} \cdot 5^{14} \cdot 13^{8} \) |
$3.04707$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$4$ |
\( 2^{5} \) |
$1$ |
$0.295748906$ |
2.365991253 |
\( -\frac{4789923264}{2640625} a + \frac{673064048}{2640625} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( -529 i + 10\) , \( 4686 i - 2154\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-529i+10\right){x}+4686i-2154$ |
| 84500.9-b4 |
84500.9-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
84500.9 |
\( 2^{2} \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{4} \cdot 5^{14} \cdot 13^{8} \) |
$3.04707$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.295748906$ |
1.774493439 |
\( -\frac{4789923264}{2640625} a + \frac{673064048}{2640625} \) |
\( \bigl[i + 1\) , \( 1\) , \( i + 1\) , \( 138 i - 510\) , \( 3785 i - 3842\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(138i-510\right){x}+3785i-3842$ |
*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.
