Cremona's table of elliptic curves

42135 = 3 · 5 · 53²

Field	Data	Notes
Atkin-Lehner	3- 5- 53+	Signs for the Atkin-Lehner involutions
Class	42135i	Isogeny class
Conductor	42135	Conductor
∏ cp	126	Product of Tamagawa factors cp
deg	653184	Modular degree for the optimal curve
Δ	85020637000078125 = 318 · 57 · 532	Discriminant
Eigenvalues	0 3- 5-  4 -4  0  2  7	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-525265,145678306]	[a1,a2,a3,a4,a6]
Generators	[470:1687:1]	Generators of the group modulo torsion
j	5705690236075638784/30267225703125	j-invariant
L	7.2967691988176	L(r)(E,1)/r!
Ω	0.34283714181484	Real period
R	0.16891654839588	Regulator
r	1	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	126405l1 42135b1	Quadratic twists by: -3 53

Hecke Eigenvalues for elliptic curve 42135i1

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	-	-	4	-4	0	2	7	-4	-9	9	-10	-3	-6	-6	+	-13	11	0	12	-16	3	18	3	-6

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Quadratic twists for elliptic curve 42135i1

-3	53
126405l1	42135b1

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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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