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
42250.7-d2 42250.7-d $2$
$5$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
42250.7
\( 2 \cdot 5^{3} \cdot 13^{2} \)
\( 2^{7} \cdot 5^{15} \cdot 13^{9} \)
$2.56227$
$(a+1), (-a-2), (2a+1), (-3a-2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $5$
5B $1$
\( 2 \cdot 5 \)
$0.867824319$
$0.178415783$
3.096671122
\( \frac{40716883}{50000} a + \frac{60021669}{50000} \)
\( \bigl[i\) , \( -i + 1\) , \( 1\) , \( -1388 i + 25\) , \( -625 i - 16719\bigr] \) ${y}^2+i{x}{y}+{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-1388i+25\right){x}-625i-16719$
42250.7-k2 42250.7-k $2$
$5$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
42250.7
\( 2 \cdot 5^{3} \cdot 13^{2} \)
\( 2^{7} \cdot 5^{9} \cdot 13^{3} \)
$2.56227$
$(a+1), (-a-2), (2a+1), (-3a-2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $5$
5B $1$
\( 2 \cdot 3 \cdot 5 \cdot 7 \)
$0.010235848$
$1.438434034$
6.183908989
\( \frac{40716883}{50000} a + \frac{60021669}{50000} \)
\( \bigl[1\) , \( i\) , \( 1\) , \( -11 i - 19\) , \( 24 i + 1\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-11i-19\right){x}+24i+1$
Download
displayed columns for
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.
