Elliptic curves over \(\Q(\sqrt{-1}) \) of conductor 2025.1

Base field	Conductor norm	Rank*	Torsion order	CM discriminant
Base field degree/signature	Bad \(p\)	$\Q$-curves	Torsion structure	CM
Analytic order of Ш*	Cyclic isogeny degree	Isogeny class size	Reduction	Galois image
j-invariant	Regulator*	Curves per isogeny class	Isogeny class degree	Nonmax$\ \ell$

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Results (3 matches)

 

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
2025.1-CMc1	2025.1-CMc	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	2025.1	\( 3^{4} \cdot 5^{2} \)	\( 3^{18} \cdot 5^{9} \)	$1.19888$	$(-a-2), (3)$	$0$	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓			$1$	\( 2^{2} \)	$1$	$0.791416409$	0.791416409	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( i\) , \( -14 i + 74\) , \( 37 i + 7\bigr] \)	${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(-14i+74\right){x}+37i+7$
2025.1-CMb1	2025.1-CMb	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	2025.1	\( 3^{4} \cdot 5^{2} \)	\( 3^{12} \cdot 5^{3} \)	$1.19888$	$(-a-2), (3)$	$0$	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$5$	5Cs.4.1	$1$	\( 2^{2} \)	$1$	$3.065142573$	3.065142573	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( 1\) , \( -5 i + 1\) , \( i + 2\bigr] \)	${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-5i+1\right){x}+i+2$
2025.1-CMa1	2025.1-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	2025.1	\( 3^{4} \cdot 5^{2} \)	\( 3^{6} \cdot 5^{9} \)	$1.19888$	$(-a-2), (3)$	$0$	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓			$1$	\( 2^{2} \)	$1$	$2.374249228$	2.374249228	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( i\) , \( -2 i + 8\) , \( 4 i + 1\bigr] \)	${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(-2i+8\right){x}+4i+1$

 

  *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.