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
15250.5-e2 15250.5-e $2$
$5$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
15250.5
\( 2 \cdot 5^{3} \cdot 61 \)
\( 2^{5} \cdot 5^{7} \cdot 61 \)
$1.98603$
$(a+1), (-a-2), (2a+1), (-6a-5)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $5$
5B.1.1 $1$
\( 5^{2} \)
$1$
$2.616191120$
2.616191120
\( \frac{3415336683}{1525000} a + \frac{13679218069}{1525000} \)
\( \bigl[i\) , \( 0\) , \( i + 1\) , \( 5 i + 9\) , \( -8 i + 8\bigr] \) ${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+\left(5i+9\right){x}-8i+8$
76250.5-a2 76250.5-a $2$
$5$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
76250.5
\( 2 \cdot 5^{4} \cdot 61 \)
\( 2^{5} \cdot 5^{19} \cdot 61 \)
$2.96981$
$(a+1), (-a-2), (2a+1), (-6a-5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $5$
5B.1.4 $1$
\( 2^{2} \)
$0.647267481$
$0.523238224$
2.709400698
\( \frac{3415336683}{1525000} a + \frac{13679218069}{1525000} \)
\( \bigl[i\) , \( -1\) , \( i + 1\) , \( 137 i + 213\) , \( -938 i + 1000\bigr] \) ${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(137i+213\right){x}-938i+1000$
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Pari/GP
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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.
