Cremona's table of elliptic curves

75088 = 2⁴ · 13 · 19²

Field	Data	Notes
Atkin-Lehner	2+ 13+ 19+	Signs for the Atkin-Lehner involutions
Class	75088d	Isogeny class
Conductor	75088	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	111686084453685248 = 211 · 132 · 199	Discriminant
Eigenvalues	2+  2  0  2  4 13+ -2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-262928,49426208]	[a1,a2,a3,a4,a6]
Generators	[-154028:3004716:343]	Generators of the group modulo torsion
j	3041750/169	j-invariant
L	10.614075210912	L(r)(E,1)/r!
Ω	0.32847055194721	Real period
R	8.0784069892888	Regulator
r	1	Rank of the group of rational points
S	1.0000000000385	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	37544i2 75088g2	Quadratic twists by: -4 -19

Hecke Eigenvalues for elliptic curve 75088d2

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

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Quadratic twists for elliptic curve 75088d2

-4	-19
37544i2	75088g2

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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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