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	75088v	Isogeny class
Conductor	75088	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	155520	Modular degree for the optimal curve
Δ	-67119041138032 = -1 · 24 · 13 · 199	Discriminant
Eigenvalues	2- -2  0 -2  0 13+ -3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-6618,-447533]	[a1,a2,a3,a4,a6]
Generators	[2571:130321:1]	Generators of the group modulo torsion
j	-42592000/89167	j-invariant
L	2.4471176407904	L(r)(E,1)/r!
Ω	0.248246407693	Real period
R	4.9288077596081	Regulator
r	1	Rank of the group of rational points
S	0.99999999988815	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	18772c1 3952i1	Quadratic twists by: -4 -19

Hecke Eigenvalues for elliptic curve 75088v1

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	0	+	-3	-	-3	-6	-1	7	-9	-11	-6	-6	9	-1	11	12	8	-10	6	-6	-11

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Quadratic twists for elliptic curve 75088v1

-4	-19
18772c1	3952i1

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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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