Elliptic curves over \(\Q(\sqrt{-103}) \) of conductor 576.4

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 103

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
576.4-a1	576.4-a	$6$	$8$	\(\Q(\sqrt{-103}) \)	$2$	$[0, 1]$	576.4	\( 2^{6} \cdot 3^{2} \)	\( 2^{22} \cdot 3^{16} \)	$4.44286$	$(2,a), (2,a+1), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{3} \)	$1$	$0.908836754$	0.358201385	\( \frac{207646}{6561} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( 16\) , \( -180\bigr] \)	${y}^2={x}^3-{x}^2+16{x}-180$
576.4-a2	576.4-a	$6$	$8$	\(\Q(\sqrt{-103}) \)	$2$	$[0, 1]$	576.4	\( 2^{6} \cdot 3^{2} \)	\( 2^{8} \cdot 3^{2} \)	$4.44286$	$(2,a), (2,a+1), (3)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{2} \)	$1$	$7.270694035$	0.358201385	\( \frac{2048}{3} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \)	${y}^2={x}^3-{x}^2+{x}$
576.4-a3	576.4-a	$6$	$8$	\(\Q(\sqrt{-103}) \)	$2$	$[0, 1]$	576.4	\( 2^{6} \cdot 3^{2} \)	\( 2^{16} \cdot 3^{4} \)	$4.44286$	$(2,a), (2,a+1), (3)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{5} \)	$1$	$3.635347017$	0.358201385	\( \frac{35152}{9} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( 4\bigr] \)	${y}^2={x}^3-{x}^2-4{x}+4$
576.4-a4	576.4-a	$6$	$8$	\(\Q(\sqrt{-103}) \)	$2$	$[0, 1]$	576.4	\( 2^{6} \cdot 3^{2} \)	\( 2^{20} \cdot 3^{8} \)	$4.44286$	$(2,a), (2,a+1), (3)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{4} \)	$1$	$1.817673508$	0.358201385	\( \frac{1556068}{81} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -24\) , \( -36\bigr] \)	${y}^2={x}^3-{x}^2-24{x}-36$
576.4-a5	576.4-a	$6$	$8$	\(\Q(\sqrt{-103}) \)	$2$	$[0, 1]$	576.4	\( 2^{6} \cdot 3^{2} \)	\( 2^{20} \cdot 3^{2} \)	$4.44286$	$(2,a), (2,a+1), (3)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	\( 2^{2} \)	$1$	$1.817673508$	0.358201385	\( \frac{28756228}{3} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -64\) , \( 220\bigr] \)	${y}^2={x}^3-{x}^2-64{x}+220$
576.4-a6	576.4-a	$6$	$8$	\(\Q(\sqrt{-103}) \)	$2$	$[0, 1]$	576.4	\( 2^{6} \cdot 3^{2} \)	\( 2^{22} \cdot 3^{4} \)	$4.44286$	$(2,a), (2,a+1), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	\( 2 \)	$1$	$0.908836754$	0.358201385	\( \frac{3065617154}{9} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -384\) , \( -2772\bigr] \)	${y}^2={x}^3-{x}^2-384{x}-2772$

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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.