Elliptic curves over \(\Q(\sqrt{-10}) \) of conductor 361.2

The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 1000 over imaginary quadratic fields with absolute discriminant 40

Note: The completeness Only modular elliptic curves are included

Results (6 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
361.2-a1	361.2-a	$3$	$9$	\(\Q(\sqrt{-10}) \)	$2$	$[0, 1]$	361.2	\( 19^{2} \)	\( 2^{12} \cdot 19^{2} \)	$2.46346$	$(a+3), (a-3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3Cs	$9$	\( 1 \)	$0.595904332$	$0.935309008$	3.172518514	\( -\frac{50357871050752}{19} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( -3077\) , \( 64681\bigr] \)	${y}^2={x}^3+{x}^2-3077{x}+64681$
361.2-a2	361.2-a	$3$	$9$	\(\Q(\sqrt{-10}) \)	$2$	$[0, 1]$	361.2	\( 19^{2} \)	\( 2^{12} \cdot 19^{6} \)	$2.46346$	$(a+3), (a-3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3Cs	$1$	\( 3^{2} \)	$0.198634777$	$2.805927025$	3.172518514	\( -\frac{89915392}{6859} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( -37\) , \( 81\bigr] \)	${y}^2={x}^3+{x}^2-37{x}+81$
361.2-a3	361.2-a	$3$	$9$	\(\Q(\sqrt{-10}) \)	$2$	$[0, 1]$	361.2	\( 19^{2} \)	\( 2^{12} \cdot 19^{2} \)	$2.46346$	$(a+3), (a-3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3Cs	$1$	\( 1 \)	$0.595904332$	$8.417781075$	3.172518514	\( \frac{32768}{19} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( 3\) , \( 1\bigr] \)	${y}^2={x}^3+{x}^2+3{x}+1$
361.2-b1	361.2-b	$3$	$9$	\(\Q(\sqrt{-10}) \)	$2$	$[0, 1]$	361.2	\( 19^{2} \)	\( 19^{2} \)	$2.46346$	$(a+3), (a-3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3Cs.1.1	$1$	\( 1 \)	$6.006027384$	$0.935309008$	3.552813586	\( -\frac{50357871050752}{19} \)	\( \bigl[0\) , \( 1\) , \( 1\) , \( -769\) , \( -8470\bigr] \)	${y}^2+{y}={x}^3+{x}^2-769{x}-8470$
361.2-b2	361.2-b	$3$	$9$	\(\Q(\sqrt{-10}) \)	$2$	$[0, 1]$	361.2	\( 19^{2} \)	\( 19^{6} \)	$2.46346$	$(a+3), (a-3)$	$1$	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3Cs.1.1	$1$	\( 3^{2} \)	$2.002009128$	$2.805927025$	3.552813586	\( -\frac{89915392}{6859} \)	\( \bigl[0\) , \( 1\) , \( 1\) , \( -9\) , \( -15\bigr] \)	${y}^2+{y}={x}^3+{x}^2-9{x}-15$
361.2-b3	361.2-b	$3$	$9$	\(\Q(\sqrt{-10}) \)	$2$	$[0, 1]$	361.2	\( 19^{2} \)	\( 19^{2} \)	$2.46346$	$(a+3), (a-3)$	$1$	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3Cs.1.1	$1$	\( 1 \)	$6.006027384$	$8.417781075$	3.552813586	\( \frac{32768}{19} \)	\( \bigl[0\) , \( 1\) , \( 1\) , \( 1\) , \( 0\bigr] \)	${y}^2+{y}={x}^3+{x}^2+{x}$

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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.