Elliptic curves over \(\Q(\sqrt{-11}) \) of conductor 46656.5

The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 50000 over imaginary quadratic fields with absolute discriminant 11

Note: The completeness Only modular elliptic curves are included

Results (4 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
46656.5-a1	46656.5-a	$1$	$1$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	46656.5	\( 2^{6} \cdot 3^{6} \)	\( 2^{16} \cdot 3^{14} \)	$4.35574$	$(-a), (a-1), (2)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cn	$1$	\( 2^{4} \cdot 3 \)	$0.046939283$	$1.510666679$	8.209940070	\( -\frac{1024}{9} a + \frac{16384}{9} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 12 a - 12\) , \( -4 a - 8\bigr] \)	${y}^2={x}^{3}+\left(12a-12\right){x}-4a-8$
46656.5-b1	46656.5-b	$1$	$1$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	46656.5	\( 2^{6} \cdot 3^{6} \)	\( 2^{16} \cdot 3^{10} \)	$4.35574$	$(-a), (a-1), (2)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2Cn	$1$	\( 2^{3} \)	$0.217888942$	$1.926513379$	8.100108780	\( 9216 a \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -12 a\) , \( -20 a + 24\bigr] \)	${y}^2={x}^{3}-12a{x}-20a+24$
46656.5-c1	46656.5-c	$1$	$1$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	46656.5	\( 2^{6} \cdot 3^{6} \)	\( 2^{8} \cdot 3^{10} \)	$4.35574$	$(-a), (a-1), (2)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2Cn	$1$	\( 2 \)	$0.582269776$	$3.245316568$	4.558006702	\( 2048 a + 4096 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 6\) , \( 3 a - 2\bigr] \)	${y}^2={x}^{3}+6{x}+3a-2$
46656.5-d1	46656.5-d	$1$	$1$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	46656.5	\( 2^{6} \cdot 3^{6} \)	\( 2^{8} \cdot 3^{18} \)	$4.35574$	$(-a), (a-1), (2)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2Cn	$1$	\( 2 \)	$1.797265475$	$1.637056636$	7.096914626	\( 512 a - 1280 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -6 a + 15\) , \( -14 a - 19\bigr] \)	${y}^2={x}^{3}+\left(-6a+15\right){x}-14a-19$

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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.