Elliptic curves over \(\Q(\sqrt{-2}) \) of conductor 387.5

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 8

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
387.5-a1	387.5-a	$1$	$1$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	387.5	\( 3^{2} \cdot 43 \)	\( 3^{7} \cdot 43 \)	$1.12101$	$(a-1), (-3a-5)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$							$1$	\( 2^{2} \)	$0.019578494$	$5.275237659$	0.584246746	\( -\frac{4096}{129} a + \frac{241664}{129} \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( -a + 1\) , \( 0\bigr] \)	${y}^2+{y}={x}^{3}+\left(-a+1\right){x}$
387.5-b1	387.5-b	$3$	$9$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	387.5	\( 3^{2} \cdot 43 \)	\( 3^{15} \cdot 43 \)	$1.12101$	$(a-1), (-3a-5)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B.1.2	$1$	\( 2^{2} \)	$0.115788454$	$2.345414412$	1.536242707	\( \frac{3128360960}{846369} a - \frac{4018143232}{846369} \)	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -4 a - 11\) , \( -10 a - 7\bigr] \)	${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a-11\right){x}-10a-7$
387.5-b2	387.5-b	$3$	$9$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	387.5	\( 3^{2} \cdot 43 \)	\( 3^{9} \cdot 43^{3} \)	$1.12101$	$(a-1), (-3a-5)$	$1$	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3Cs.1.1	$1$	\( 2^{2} \cdot 3 \)	$0.347365362$	$2.345414412$	1.536242707	\( -\frac{340295680}{2146689} a + \frac{3946938368}{2146689} \)	\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( -9\) , \( -2 a\bigr] \)	${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}-9{x}-2a$
387.5-b3	387.5-b	$3$	$9$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	387.5	\( 3^{2} \cdot 43 \)	\( 3^{7} \cdot 43 \)	$1.12101$	$(a-1), (-3a-5)$	$1$	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B.1.1	$1$	\( 2^{2} \)	$1.042096086$	$2.345414412$	1.536242707	\( \frac{2235072512}{129} a + \frac{2686877696}{129} \)	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -20 a + 35\) , \( 63 a + 97\bigr] \)	${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-20a+35\right){x}+63a+97$

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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.