| 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 |
| 1800.3-a1 |
1800.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1800.3 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{11} \cdot 3^{2} \cdot 5^{10} \) |
$1.16409$ |
$(a+1), (2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1.583374277$ |
1.583374277 |
\( \frac{2401}{3} a + \frac{343}{3} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 14 i + 4\) , \( 26 i + 20\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+\left(14i+4\right){x}+26i+20$ |
| 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 |
\( \frac{2401}{3} a + \frac{343}{3} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( -3 i + 2\) , \( 2 i + 1\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-3i+2\right){x}+2i+1$ |
| 16200.3-a1 |
16200.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16200.3 |
\( 2^{3} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{11} \cdot 3^{14} \cdot 5^{10} \) |
$2.01626$ |
$(a+1), (2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$0.527791425$ |
1.055582851 |
\( \frac{2401}{3} a + \frac{343}{3} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( 125 i + 36\) , \( 738 i + 414\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(125i+36\right){x}+738i+414$ |
| 32400.3-f1 |
32400.3-f |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
32400.3 |
\( 2^{4} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{11} \cdot 3^{14} \cdot 5^{4} \) |
$2.39775$ |
$(a+1), (2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{3} \) |
$0.232411670$ |
$1.180177506$ |
4.388592414 |
\( \frac{2401}{3} a + \frac{343}{3} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -22 i + 15\) , \( 63 i + 64\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-22i+15\right){x}+63i+64$ |
| 45000.3-j1 |
45000.3-j |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
45000.3 |
\( 2^{3} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{11} \cdot 3^{2} \cdot 5^{10} \) |
$2.60299$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1.583374277$ |
1.583374277 |
\( \frac{2401}{3} a + \frac{343}{3} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( i - 15\) , \( -26 i - 31\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(i-15\right){x}-26i-31$ |
| 57600.3-c1 |
57600.3-c |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
57600.3 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{23} \cdot 3^{2} \cdot 5^{10} \) |
$2.76869$ |
$(a+1), (2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$0.791687138$ |
1.583374277 |
\( \frac{2401}{3} a + \frac{343}{3} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 56 i + 16\) , \( 208 i + 160\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+\left(56i+16\right){x}+208i+160$ |
| 57600.3-q1 |
57600.3-q |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
57600.3 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{23} \cdot 3^{2} \cdot 5^{4} \) |
$2.76869$ |
$(a+1), (2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1.770266259$ |
3.540532518 |
\( \frac{2401}{3} a + \frac{343}{3} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -10 i + 7\) , \( -11 i - 15\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-10i+7\right){x}-11i-15$ |
| 90000.3-m1 |
90000.3-m |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
90000.3 |
\( 2^{4} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{11} \cdot 3^{2} \cdot 5^{16} \) |
$3.09549$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$0.708106503$ |
1.416213007 |
\( \frac{2401}{3} a + \frac{343}{3} \) |
\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -58 i + 44\) , \( 246 i + 272\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-58i+44\right){x}+246i+272$ |
*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.
