Elliptic curves over \(\Q(\sqrt{-1}) \) of conductor 25.1

The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 100000 over imaginary quadratic fields with absolute discriminant 4

Note: The completeness Only modular elliptic curves are included

Results (unique match)

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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
25.1-CMa1	25.1-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	25.1	\( 5^{2} \)	\( 5^{3} \)	$0.39963$	$(-a-2)$	0	$\Z/10\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$5$	5Cs.1.1	$1$	\( 2 \)	$1$	$9.195427721$	0.183908554	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( 1\) , \( -i - 1\) , \( 0\bigr] \)	${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-i-1\right){x}$

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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.