Cremona's table of elliptic curves

4012 = 2² · 17 · 59

Field	Data	Notes
Atkin-Lehner	2- 17- 59+	Signs for the Atkin-Lehner involutions
Class	4012c	Isogeny class
Conductor	4012	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	2208	Modular degree for the optimal curve
Δ	-78843824 = -1 · 24 · 174 · 59	Discriminant
Eigenvalues	2- -3 -1 -5 -2  4 17- -3	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-28,-431]	[a1,a2,a3,a4,a6]
Generators	[10:17:1]	Generators of the group modulo torsion
j	-151732224/4927739	j-invariant
L	1.507805289599	L(r)(E,1)/r!
Ω	0.84012461285424	Real period
R	0.14956167082527	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	16048bd1 64192be1 36108c1 100300e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4012c1

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
-	-3	-1	-5	-2	4	-	-3	-4	-3	8	0	3	4	8	7	+	10	10	-8	-10	13	-4	14	2

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Quadratic twists for elliptic curve 4012c1

-4	8	-3	5	17
16048bd1	64192be1	36108c1	100300e1	68204b1

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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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