Elliptic curves over \(\Q(\sqrt{-1}) \) of conductor 60025.1

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
60025.1-CMc1	60025.1-CMc	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	60025.1	\( 5^{2} \cdot 7^{4} \)	\( 5^{3} \cdot 7^{18} \)	$2.79738$	$(-a-2), (7)$	$0$	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓			$9$	\( 2^{2} \)	$1$	$0.496506427$	4.468557847	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( 1\) , \( 171 i - 87\) , \( -43 i - 86\bigr] \)	${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(171i-87\right){x}-43i-86$
60025.1-CMb1	60025.1-CMb	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	60025.1	\( 5^{2} \cdot 7^{4} \)	\( 5^{3} \cdot 7^{12} \)	$2.79738$	$(-a-2), (7)$	$0$	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$5$	5Cs.4.1	$1$	\( 2^{2} \)	$1$	$1.313632531$	1.313632531	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( 1\) , \( -25 i + 11\) , \( 6 i + 12\bigr] \)	${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-25i+11\right){x}+6i+12$
60025.1-CMa1	60025.1-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	60025.1	\( 5^{2} \cdot 7^{4} \)	\( 5^{3} \cdot 7^{6} \)	$2.79738$	$(-a-2), (7)$	$0$	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓			$1$	\( 2^{2} \)	$1$	$3.475544992$	3.475544992	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( 1\) , \( 3 i - 3\) , \( -i - 2\bigr] \)	${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(3i-3\right){x}-i-2$

 

  *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.