| 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 |
| 3600.3-a1 |
3600.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3600.3 |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{11} \cdot 3^{2} \cdot 5^{4} \) |
$1.38434$ |
$(a+1), (2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3 \) |
$0.021599395$ |
$3.540532518$ |
1.835360692 |
\( \frac{2401}{3} a + \frac{343}{3} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( -3 i + 2\) , \( 2 i + 1\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-3i+2\right){x}+2i+1$ |
| 3600.3-b1 |
3600.3-b |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3600.3 |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{17} \cdot 3^{2} \cdot 5^{8} \) |
$1.38434$ |
$(a+1), (2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.056808315$ |
$1.480066113$ |
2.017921495 |
\( -\frac{1039}{24} a + \frac{13913}{24} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( i + 1\) , \( 5 i - 14\) , \( 16 i + 21\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(5i-14\right){x}+16i+21$ |
| 3600.3-b2 |
3600.3-b |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3600.3 |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{13} \cdot 3^{10} \cdot 5^{4} \) |
$1.38434$ |
$(a+1), (2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2^{2} \cdot 3 \cdot 5 \) |
$0.011361663$ |
$1.480066113$ |
2.017921495 |
\( -\frac{957521}{486} a + \frac{776647}{486} \) |
\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( -3 i + 23\) , \( 36 i + 21\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-3i+23\right){x}+36i+21$ |
| 3600.3-c1 |
3600.3-c |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3600.3 |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{16} \cdot 5^{6} \) |
$1.38434$ |
$(a+1), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.812888305$ |
1.625776610 |
\( \frac{207646}{6561} \) |
\( \bigl[i + 1\) , \( -1\) , \( i + 1\) , \( -17 i + 12\) , \( 247 i - 45\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(-17i+12\right){x}+247i-45$ |
| 3600.3-c2 |
3600.3-c |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3600.3 |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 5^{6} \) |
$1.38434$ |
$(a+1), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.251553221$ |
1.625776610 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 2 i - 2\) , \( 2 i + 3\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(2i-2\right){x}+2i+3$ |
| 3600.3-c3 |
3600.3-c |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3600.3 |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 5^{6} \) |
$1.38434$ |
$(a+1), (2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3.251553221$ |
1.625776610 |
\( \frac{35152}{9} \) |
\( \bigl[i + 1\) , \( -1\) , \( i + 1\) , \( 3 i - 3\) , \( -6 i + 1\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(3i-3\right){x}-6i+1$ |
| 3600.3-c4 |
3600.3-c |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3600.3 |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 5^{6} \) |
$1.38434$ |
$(a+1), (2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.625776610$ |
1.625776610 |
\( \frac{1556068}{81} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( i + 1\) , \( 23 i - 18\) , \( -50 i + 9\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(23i-18\right){x}-50i+9$ |
| 3600.3-c5 |
3600.3-c |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3600.3 |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 5^{6} \) |
$1.38434$ |
$(a+1), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.625776610$ |
1.625776610 |
\( \frac{28756228}{3} \) |
\( \bigl[i + 1\) , \( -1\) , \( i + 1\) , \( 63 i - 48\) , \( -303 i + 55\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(63i-48\right){x}-303i+55$ |
| 3600.3-c6 |
3600.3-c |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3600.3 |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{4} \cdot 5^{6} \) |
$1.38434$ |
$(a+1), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.812888305$ |
1.625776610 |
\( \frac{3065617154}{9} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( i + 1\) , \( 383 i - 288\) , \( -3812 i + 693\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(383i-288\right){x}-3812i+693$ |
*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.
