| 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-b5 |
3400.4-b |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3400.4 |
\( 2^{3} \cdot 5^{2} \cdot 17 \) |
\( 2^{8} \cdot 5^{10} \cdot 17 \) |
$1.36470$ |
$(a+1), (-a-2), (2a+1), (a-4)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$1.789627193$ |
1.789627193 |
\( \frac{2845155328}{6640625} a + \frac{8254109696}{6640625} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( 14 i - 2\) , \( -8 i + 1\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(14i-2\right){x}-8i+1$ |
| 34000.4-a5 |
34000.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
34000.4 |
\( 2^{4} \cdot 5^{3} \cdot 17 \) |
\( 2^{8} \cdot 5^{16} \cdot 17 \) |
$2.42682$ |
$(a+1), (-a-2), (2a+1), (a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.800345611$ |
0.800345611 |
\( \frac{2845155328}{6640625} a + \frac{8254109696}{6640625} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( -32 i + 59\) , \( 123 i - 55\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+\left(-32i+59\right){x}+123i-55$ |
| 34000.6-b5 |
34000.6-b |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
34000.6 |
\( 2^{4} \cdot 5^{3} \cdot 17 \) |
\( 2^{8} \cdot 5^{16} \cdot 17 \) |
$2.42682$ |
$(a+1), (-a-2), (2a+1), (a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.146032671$ |
$0.800345611$ |
3.668888877 |
\( \frac{2845155328}{6640625} a + \frac{8254109696}{6640625} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -48 i - 47\) , \( -134 i + 76\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-48i-47\right){x}-134i+76$ |
| 57800.6-b5 |
57800.6-b |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
57800.6 |
\( 2^{3} \cdot 5^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 5^{10} \cdot 17^{7} \) |
$2.77109$ |
$(a+1), (-a-2), (2a+1), (a-4)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.575901732$ |
$0.434048349$ |
3.999507146 |
\( \frac{2845155328}{6640625} a + \frac{8254109696}{6640625} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( -216 i - 77\) , \( -261 i + 979\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+\left(-216i-77\right){x}-261i+979$ |
| 85000.6-d5 |
85000.6-d |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
85000.6 |
\( 2^{3} \cdot 5^{4} \cdot 17 \) |
\( 2^{8} \cdot 5^{22} \cdot 17 \) |
$3.05157$ |
$(a+1), (-a-2), (2a+1), (a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.357925438$ |
1.431701754 |
\( \frac{2845155328}{6640625} a + \frac{8254109696}{6640625} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( 334 i - 50\) , \( 1576 i - 901\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(334i-50\right){x}+1576i-901$ |
*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.
