Cremona's table of elliptic curves

380 = 2² · 5 · 19

Field	Data	Notes
Atkin-Lehner	2- 5+ 19-	Signs for the Atkin-Lehner involutions
Class	380a	Isogeny class
Conductor	380	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	121600 = 28 · 52 · 19	Discriminant
Eigenvalues	2-  0 5+ -2 -4 -4  6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-103,-402]	[a1,a2,a3,a4,a6]
Generators	[14:30:1]	Generators of the group modulo torsion
j	472058064/475	j-invariant
L	1.6365169446457	L(r)(E,1)/r!
Ω	1.4987061355956	Real period
R	2.1839063786783	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1520f2 6080g2 3420d2 1900c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 380a2

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	0	+	-2	-4	-4	6	-	-2	-6	-8	4	6	-6	6	8	-12	6	0	0	-10	-8	14	14	16

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Quadratic twists for elliptic curve 380a2

-4	8	-3	5	-7	-11	13	17	-19
1520f2	6080g2	3420d2	1900c2	18620j2	45980a2	64220h2	109820k2	7220b2

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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