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
42250.6-d2 42250.6-d $2$
$5$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
42250.6
\( 2 \cdot 5^{3} \cdot 13^{2} \)
\( 2^{7} \cdot 5^{15} \cdot 13^{9} \)
$2.56227$
$(a+1), (-a-2), (2a+1), (2a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $5$
5B $1$
\( 2 \cdot 5 \)
$0.867824319$
$0.178415783$
3.096671122
\( -\frac{40716883}{50000} a + \frac{60021669}{50000} \)
\( \bigl[1\) , \( -i - 1\) , \( i\) , \( 1387 i + 25\) , \( -625 i + 16719\bigr] \) ${y}^2+{x}{y}+i{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(1387i+25\right){x}-625i+16719$
42250.6-k2 42250.6-k $2$
$5$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
42250.6
\( 2 \cdot 5^{3} \cdot 13^{2} \)
\( 2^{7} \cdot 5^{9} \cdot 13^{3} \)
$2.56227$
$(a+1), (-a-2), (2a+1), (2a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $5$
5B $1$
\( 2 \cdot 3 \cdot 5 \cdot 7 \)
$0.010235848$
$1.438434034$
6.183908989
\( -\frac{40716883}{50000} a + \frac{60021669}{50000} \)
\( \bigl[i\) , \( i\) , \( i\) , \( 11 i - 18\) , \( 24 i - 1\bigr] \) ${y}^2+i{x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(11i-18\right){x}+24i-1$
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*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.
