Elliptic curves over \(\Q(\sqrt{-1}) \) of conductor 7225.1

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 (5 matches)

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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
7225.1-CMc1	7225.1-CMc	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	7225.1	\( 5^{2} \cdot 17^{2} \)	\( 5^{3} \cdot 17^{9} \)	$1.64770$	$(-a-2), (a+4)$	$0 \le r \le 2$	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓			$4$	\( 2^{2} \)	$1$	$1.098336064$	4.393344256	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( i\) , \( 36 i + 14\) , \( 7 i - 18\bigr] \)	${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(36i+14\right){x}+7i-18$
7225.1-CMb1	7225.1-CMb	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	7225.1	\( 5^{2} \cdot 17^{2} \)	\( 5^{3} \cdot 17^{6} \)	$1.64770$	$(-a-2), (a+4)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$5$	5Cs.4.1	$1$	\( 2^{3} \)	$1$	$2.230218809$	4.460437619	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( 1\) , \( 5 i - 9\) , \( -4 i - 3\bigr] \)	${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(5i-9\right){x}-4i-3$
7225.1-CMa1	7225.1-CMa	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	7225.1	\( 5^{2} \cdot 17^{2} \)	\( 5^{3} \cdot 17^{3} \)	$1.64770$	$(-a-2), (a+4)$	$2$	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓			$1$	\( 2^{2} \)	$0.083859627$	$4.528555605$	1.519051940	\( 1728 \)	\( \bigl[i + 1\) , \( i\) , \( i\) , \( -2 i - 2\) , \( -i + 1\bigr] \)	${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(-2i-2\right){x}-i+1$
7225.1-a1	7225.1-a	$2$	$2$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	7225.1	\( 5^{2} \cdot 17^{2} \)	\( 5^{9} \cdot 17^{10} \)	$1.64770$	$(-a-2), (a+4)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{3} \)	$1$	$0.385027262$	0.770054525	\( \frac{34677248}{83521} a + \frac{158300864}{83521} \)	\( \bigl[i + 1\) , \( i - 1\) , \( i\) , \( 211 i + 248\) , \( 77 i - 1279\bigr] \)	${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(211i+248\right){x}+77i-1279$
7225.1-a2	7225.1-a	$2$	$2$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	7225.1	\( 5^{2} \cdot 17^{2} \)	\( 5^{9} \cdot 17^{8} \)	$1.64770$	$(-a-2), (a+4)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{3} \)	$1$	$0.385027262$	0.770054525	\( \frac{291200512}{289} a + \frac{204122816}{289} \)	\( \bigl[i + 1\) , \( 0\) , \( i\) , \( -778 i - 765\) , \( -13002 i - 5018\bigr] \)	${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+\left(-778i-765\right){x}-13002i-5018$

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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.