Elliptic curves over \(\Q(\sqrt{-1}) \) of conductor 3250.4

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 (3 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
3250.4-a1	3250.4-a	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	3250.4	\( 2 \cdot 5^{3} \cdot 13 \)	\( 2^{17} \cdot 5^{11} \cdot 13 \)	$1.34940$	$(a+1), (-a-2), (2a+1), (2a+3)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$							$1$	\( 1 \)	$1$	$0.939702506$	0.939702506	\( \frac{19040273}{33280} a - \frac{28339689}{33280} \)	\( \bigl[i\) , \( i\) , \( i + 1\) , \( 39 i + 19\) , \( -52 i - 186\bigr] \)	${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(39i+19\right){x}-52i-186$
3250.4-b1	3250.4-b	$2$	$3$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	3250.4	\( 2 \cdot 5^{3} \cdot 13 \)	\( 2^{3} \cdot 5^{11} \cdot 13 \)	$1.34940$	$(a+1), (-a-2), (2a+1), (2a+3)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B.1.1	$1$	\( 3^{2} \)	$1$	$2.113453741$	2.113453741	\( \frac{2124209}{6500} a - \frac{5592087}{6500} \)	\( \bigl[i\) , \( i + 1\) , \( i + 1\) , \( -7 i + 5\) , \( -4 i - 12\bigr] \)	${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-7i+5\right){x}-4i-12$
3250.4-b2	3250.4-b	$2$	$3$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	3250.4	\( 2 \cdot 5^{3} \cdot 13 \)	\( 2 \cdot 5^{17} \cdot 13^{3} \)	$1.34940$	$(a+1), (-a-2), (2a+1), (2a+3)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B.1.2	$1$	\( 3 \)	$1$	$0.704484580$	2.113453741	\( -\frac{1498457535463}{8582031250} a + \frac{5584902421359}{8582031250} \)	\( \bigl[i\) , \( i + 1\) , \( i + 1\) , \( 58 i - 40\) , \( 97 i + 245\bigr] \)	${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(58i-40\right){x}+97i+245$

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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.