| 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 |
| 650.4-a7 |
650.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
650.4 |
\( 2 \cdot 5^{2} \cdot 13 \) |
\( 2^{6} \cdot 5^{10} \cdot 13^{2} \) |
$0.90240$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$1.446424644$ |
1.446424644 |
\( -\frac{117057737097}{21125000} a + \frac{49160487287}{2640625} \) |
\( \bigl[1\) , \( 0\) , \( i + 1\) , \( -39 i - 1\) , \( -68 i + 60\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-39i-1\right){x}-68i+60$ |
| 16250.6-a7 |
16250.6-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.6 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{6} \cdot 5^{22} \cdot 13^{2} \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \) |
$0.982727851$ |
$0.289284928$ |
2.274306853 |
\( -\frac{117057737097}{21125000} a + \frac{49160487287}{2640625} \) |
\( \bigl[i\) , \( -1\) , \( i + 1\) , \( -963 i - 12\) , \( 8437 i - 7500\bigr] \) |
${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(-963i-12\right){x}+8437i-7500$ |
| 26000.4-f7 |
26000.4-f |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{18} \cdot 5^{16} \cdot 13^{2} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.323430382$ |
1.293721531 |
\( -\frac{117057737097}{21125000} a + \frac{49160487287}{2640625} \) |
\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -470 i + 610\) , \( 4200 i + 6900\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-470i+610\right){x}+4200i+6900$ |
| 26000.6-f7 |
26000.6-f |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.6 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{18} \cdot 5^{16} \cdot 13^{2} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{7} \) |
$1$ |
$0.323430382$ |
2.587443063 |
\( -\frac{117057737097}{21125000} a + \frac{49160487287}{2640625} \) |
\( \bigl[i + 1\) , \( -1\) , \( 0\) , \( -454 i - 622\) , \( 6360 i + 4980\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-454i-622\right){x}+6360i+4980$ |
| 42250.6-e7 |
42250.6-e |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42250.6 |
\( 2 \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{6} \cdot 5^{16} \cdot 13^{8} \) |
$2.56227$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \cdot 3 \) |
$1$ |
$0.179406896$ |
2.152882762 |
\( -\frac{117057737097}{21125000} a + \frac{49160487287}{2640625} \) |
\( \bigl[i\) , \( -i - 1\) , \( 1\) , \( -1241 i - 2173\) , \( -30671 i - 32777\bigr] \) |
${y}^2+i{x}{y}+{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-1241i-2173\right){x}-30671i-32777$ |
| 42250.9-i7 |
42250.9-i |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42250.9 |
\( 2 \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{6} \cdot 5^{16} \cdot 13^{8} \) |
$2.56227$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{7} \cdot 3 \) |
$0.741344183$ |
$0.179406896$ |
6.384108451 |
\( -\frac{117057737097}{21125000} a + \frac{49160487287}{2640625} \) |
\( \bigl[i\) , \( -i\) , \( i\) , \( 2434 i - 583\) , \( -41589 i - 19046\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-i{x}^{2}+\left(2434i-583\right){x}-41589i-19046$ |
| 52650.4-a7 |
52650.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52650.4 |
\( 2 \cdot 3^{4} \cdot 5^{2} \cdot 13 \) |
\( 2^{6} \cdot 3^{12} \cdot 5^{10} \cdot 13^{2} \) |
$2.70719$ |
$(a+1), (-a-2), (2a+1), (2a+3), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{7} \) |
$0.418000179$ |
$0.482141548$ |
3.224564057 |
\( -\frac{117057737097}{21125000} a + \frac{49160487287}{2640625} \) |
\( \bigl[1\) , \( -1\) , \( i + 1\) , \( -347 i - 5\) , \( 1822 i - 1620\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(-347i-5\right){x}+1822i-1620$ |
| 67600.6-a7 |
67600.6-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.6 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{18} \cdot 5^{10} \cdot 13^{8} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \) |
$2.118844312$ |
$0.200583008$ |
3.400033334 |
\( -\frac{117057737097}{21125000} a + \frac{49160487287}{2640625} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( 794 i - 1838\) , \( -20520 i + 26940\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(794i-1838\right){x}-20520i+26940$ |
| 83200.4-n7 |
83200.4-n |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
83200.4 |
\( 2^{8} \cdot 5^{2} \cdot 13 \) |
\( 2^{30} \cdot 5^{10} \cdot 13^{2} \) |
$3.03528$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.361606161$ |
1.446424644 |
\( -\frac{117057737097}{21125000} a + \frac{49160487287}{2640625} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 616 i + 8\) , \( 3840 i + 4320\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+\left(616i+8\right){x}+3840i+4320$ |
*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.
