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	4012a	Isogeny class
Conductor	4012	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1056	Modular degree for the optimal curve
Δ	-272816 = -1 · 24 · 172 · 59	Discriminant
Eigenvalues	2- -3 -3 -1 -2 -2 17+ -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-184,961]	[a1,a2,a3,a4,a6]
Generators	[38:221:1] [-6:43:1]	Generators of the group modulo torsion
j	-43058331648/17051	j-invariant
L	2.6459319378598	L(r)(E,1)/r!
Ω	3.0413457788417	Real period
R	0.14499786883099	Regulator
r	2	Rank of the group of rational points
S	0.99999999999952	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	16048v1 64192p1 36108g1 100300f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4012a1

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	-3	-1	-2	-2	+	-1	0	-9	0	-10	-3	-8	0	-1	+	-8	-6	-8	-2	-11	14	-10	8

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Quadratic twists for elliptic curve 4012a1

-4	8	-3	5	17
16048v1	64192p1	36108g1	100300f1	68204c1

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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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