| 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 |
| 3400.4-b2 |
3400.4-b |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3400.4 |
\( 2^{3} \cdot 5^{2} \cdot 17 \) |
\( 2^{4} \cdot 5^{8} \cdot 17^{2} \) |
$1.36470$ |
$(a+1), (-a-2), (2a+1), (a-4)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$1.789627193$ |
1.789627193 |
\( -\frac{18495673728}{180625} a - \frac{897072368}{36125} \) |
\( \bigl[i + 1\) , \( 1\) , \( i + 1\) , \( -34 i - 8\) , \( -84 i + 34\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(-34i-8\right){x}-84i+34$ |
| 34000.4-a2 |
34000.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
34000.4 |
\( 2^{4} \cdot 5^{3} \cdot 17 \) |
\( 2^{4} \cdot 5^{14} \cdot 17^{2} \) |
$2.42682$ |
$(a+1), (-a-2), (2a+1), (a-4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$0.800345611$ |
0.800345611 |
\( -\frac{18495673728}{180625} a - \frac{897072368}{36125} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( 134 i - 109\) , \( -854 i + 98\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(134i-109\right){x}-854i+98$ |
| 34000.6-b2 |
34000.6-b |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
34000.6 |
\( 2^{4} \cdot 5^{3} \cdot 17 \) |
\( 2^{4} \cdot 5^{14} \cdot 17^{2} \) |
$2.42682$ |
$(a+1), (-a-2), (2a+1), (a-4)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$2.292065342$ |
$0.800345611$ |
3.668888877 |
\( -\frac{18495673728}{180625} a - \frac{897072368}{36125} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 67 i + 158\) , \( 693 i - 474\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+\left(67i+158\right){x}+693i-474$ |
| 57800.6-b2 |
57800.6-b |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
57800.6 |
\( 2^{3} \cdot 5^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 5^{8} \cdot 17^{8} \) |
$2.77109$ |
$(a+1), (-a-2), (2a+1), (a-4)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1.151803464$ |
$0.434048349$ |
3.999507146 |
\( -\frac{18495673728}{180625} a - \frac{897072368}{36125} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( 433 i + 390\) , \( 1769 i - 5508\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(433i+390\right){x}+1769i-5508$ |
| 85000.6-d2 |
85000.6-d |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
85000.6 |
\( 2^{3} \cdot 5^{4} \cdot 17 \) |
\( 2^{4} \cdot 5^{20} \cdot 17^{2} \) |
$3.05157$ |
$(a+1), (-a-2), (2a+1), (a-4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.357925438$ |
1.431701754 |
\( -\frac{18495673728}{180625} a - \frac{897072368}{36125} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -833 i - 206\) , \( -8571 i + 3828\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-833i-206\right){x}-8571i+3828$ |
*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.
