Cremona's table of elliptic curves

42350 = 2 · 5² · 7 · 11²

Field	Data	Notes
Atkin-Lehner	2- 5- 7- 11-	Signs for the Atkin-Lehner involutions
Class	42350dc	Isogeny class
Conductor	42350	Conductor
∏ cp	324	Product of Tamagawa factors cp
deg	114048	Modular degree for the optimal curve
Δ	12855969280000 = 212 · 54 · 73 · 114	Discriminant
Eigenvalues	2-  1 5- 7- 11-  2  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-21238,-1180508]	[a1,a2,a3,a4,a6]
Generators	[-84:154:1]	Generators of the group modulo torsion
j	115775077825/1404928	j-invariant
L	10.960008491777	L(r)(E,1)/r!
Ω	0.39576712011126	Real period
R	0.76925207996421	Regulator
r	1	Rank of the group of rational points
S	1.0000000000003	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	42350h1 42350bk1	Quadratic twists by: 5 -11

Hecke Eigenvalues for elliptic curve 42350dc1

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
-	1	-	-	-	2	0	-4	-6	3	8	-1	6	-10	-9	6	9	-10	2	-12	-4	14	3	18	-10

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Quadratic twists for elliptic curve 42350dc1

5	-11
42350h1	42350bk1

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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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