Cremona's table of elliptic curves

1950 = 2 · 3 · 5² · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 13+	Signs for the Atkin-Lehner involutions
Class	1950v	Isogeny class
Conductor	1950	Conductor
∏ cp	160	Product of Tamagawa factors cp
Δ	11332049303250000 = 24 · 320 · 56 · 13	Discriminant
Eigenvalues	2- 3- 5+ -4 -4 13+ -2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-58488,-1851408]	[a1,a2,a3,a4,a6]
Generators	[282:-2166:1]	Generators of the group modulo torsion
j	1416134368422073/725251155408	j-invariant
L	4.4461010705517	L(r)(E,1)/r!
Ω	0.32432733279387	Real period
R	0.34271711177187	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	15600bd4 62400bh3 5850m4 78a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1950v3

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
-	-	+	-4	-4	+	-2	-8	0	6	-4	2	-10	-4	-8	10	4	-2	16	-8	-2	8	-12	14	-10

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Quadratic twists for elliptic curve 1950v3

-4	8	-3	5	-7	13
15600bd4	62400bh3	5850m4	78a3	95550hl3	25350bg3

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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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