| 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 |
| 3250.4-b2 |
3250.4-b |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3250.4 |
\( 2 \cdot 5^{3} \cdot 13 \) |
\( 2 \cdot 5^{17} \cdot 13^{3} \) |
$1.34940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$0.704484580$ |
2.113453741 |
\( -\frac{1498457535463}{8582031250} a + \frac{5584902421359}{8582031250} \) |
\( \bigl[i\) , \( i + 1\) , \( i + 1\) , \( 58 i - 40\) , \( 97 i + 245\bigr] \) |
${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(58i-40\right){x}+97i+245$ |
| 16250.6-d2 |
16250.6-d |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.6 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2 \cdot 5^{17} \cdot 13^{3} \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.421789456$ |
$0.704484580$ |
2.377153349 |
\( -\frac{1498457535463}{8582031250} a + \frac{5584902421359}{8582031250} \) |
\( \bigl[1\) , \( 1\) , \( i + 1\) , \( 22 i + 67\) , \( -178 i - 195\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(22i+67\right){x}-178i-195$ |
| 26000.4-h2 |
26000.4-h |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{13} \cdot 5^{11} \cdot 13^{3} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$0.022152176$ |
$0.787637705$ |
3.768744045 |
\( -\frac{1498457535463}{8582031250} a + \frac{5584902421359}{8582031250} \) |
\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( 54 i + 18\) , \( -160 i + 100\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(54i+18\right){x}-160i+100$ |
| 42250.6-b2 |
42250.6-b |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42250.6 |
\( 2 \cdot 5^{3} \cdot 13^{2} \) |
\( 2 \cdot 5^{11} \cdot 13^{9} \) |
$2.56227$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.801867847$ |
$0.436902789$ |
2.802706395 |
\( -\frac{1498457535463}{8582031250} a + \frac{5584902421359}{8582031250} \) |
\( \bigl[1\) , \( i + 1\) , \( i\) , \( -120 i + 139\) , \( -928 i + 894\bigr] \) |
${y}^2+{x}{y}+i{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-120i+139\right){x}-928i+894$ |
*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.
