Elliptic curves over \(\Q(\sqrt{-11}) \) of conductor 46656.3

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
46656.3-a1	46656.3-a	$1$	$1$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	46656.3	\( 2^{6} \cdot 3^{6} \)	\( 2^{16} \cdot 3^{10} \)	$4.35574$	$(-a), (a-1), (2)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2Cn	$1$	\( 2^{3} \)	$0.217888942$	$1.926513379$	8.100108780	\( -9216 a + 9216 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 12 a - 12\) , \( 20 a + 4\bigr] \)	${y}^2={x}^{3}+\left(12a-12\right){x}+20a+4$
46656.3-b1	46656.3-b	$1$	$1$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	46656.3	\( 2^{6} \cdot 3^{6} \)	\( 2^{8} \cdot 3^{10} \)	$4.35574$	$(-a), (a-1), (2)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2Cn	$1$	\( 2 \)	$0.582269776$	$3.245316568$	4.558006702	\( -2048 a + 6144 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 6\) , \( -3 a + 1\bigr] \)	${y}^2={x}^{3}+6{x}-3a+1$
46656.3-c1	46656.3-c	$1$	$1$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	46656.3	\( 2^{6} \cdot 3^{6} \)	\( 2^{16} \cdot 3^{14} \)	$4.35574$	$(-a), (a-1), (2)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cn	$1$	\( 2^{4} \cdot 3 \)	$0.046939283$	$1.510666679$	8.209940070	\( \frac{1024}{9} a + \frac{5120}{3} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -12 a\) , \( 4 a - 12\bigr] \)	${y}^2={x}^{3}-12a{x}+4a-12$
46656.3-d1	46656.3-d	$1$	$1$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	46656.3	\( 2^{6} \cdot 3^{6} \)	\( 2^{8} \cdot 3^{18} \)	$4.35574$	$(-a), (a-1), (2)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2Cn	$1$	\( 2 \)	$1.797265475$	$1.637056636$	7.096914626	\( -512 a - 768 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 6 a + 9\) , \( 14 a - 33\bigr] \)	${y}^2={x}^{3}+\left(6a+9\right){x}+14a-33$

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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.