Cremona's table of elliptic curves

3612 = 2² · 3 · 7 · 43

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 43-	Signs for the Atkin-Lehner involutions
Class	3612h	Isogeny class
Conductor	3612	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	4800	Modular degree for the optimal curve
Δ	-651322616112 = -1 · 24 · 35 · 72 · 434	Discriminant
Eigenvalues	2- 3-  0 7-  2 -6 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-4233,111492]	[a1,a2,a3,a4,a6]
Generators	[96:774:1]	Generators of the group modulo torsion
j	-524386048000000/40707663507	j-invariant
L	4.2097874354989	L(r)(E,1)/r!
Ω	0.89267801851312	Real period
R	0.4715908029763	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	14448j1 57792p1 10836i1 90300b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3612h1

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	-	2	-6	-4	4	-6	-6	-8	-6	0	-	8	-6	-4	-2	8	10	-2	-4	0	-12	6

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Quadratic twists for elliptic curve 3612h1

-4	8	-3	5	-7
14448j1	57792p1	10836i1	90300b1	25284c1

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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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