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	42350cm	Isogeny class
Conductor	42350	Conductor
∏ cp	252	Product of Tamagawa factors cp
deg	580608	Modular degree for the optimal curve
Δ	-33999257600000000 = -1 · 221 · 58 · 73 · 112	Discriminant
Eigenvalues	2- -1 5+ 7- 11- -7 -6 -5	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-198338,35054031]	[a1,a2,a3,a4,a6]
Generators	[-495:3747:1] [345:-2973:1]	Generators of the group modulo torsion
j	-456390127585249/17983078400	j-invariant
L	11.105686773301	L(r)(E,1)/r!
Ω	0.36534149020038	Real period
R	0.12062737682535	Regulator
r	2	Rank of the group of rational points
S	0.99999999999998	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8470d1 42350l1	Quadratic twists by: 5 -11

Hecke Eigenvalues for elliptic curve 42350cm1

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	+	-	-	-7	-6	-5	-9	0	2	-2	-12	-4	-6	6	9	-14	-2	0	-10	-11	9	12	-8

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Quadratic twists for elliptic curve 42350cm1

5	-11
8470d1	42350l1

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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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