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	3612c	Isogeny class
Conductor	3612	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	5591376 = 24 · 33 · 7 · 432	Discriminant
Eigenvalues	2- 3+  2 7+  2  2 -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-77,-210]	[a1,a2,a3,a4,a6]
Generators	[-5:5:1]	Generators of the group modulo torsion
j	3196715008/349461	j-invariant
L	3.372133509803	L(r)(E,1)/r!
Ω	1.6213509109615	Real period
R	1.3865530227519	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	14448bb1 57792bg1 10836e1 90300bk1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3612c1

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
-	+	2	+	2	2	-6	0	-6	0	-6	-6	6	-	-12	2	8	-4	0	-12	8	-4	8	-6	2

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Quadratic twists for elliptic curve 3612c1

-4	8	-3	5	-7
14448bb1	57792bg1	10836e1	90300bk1	25284n1

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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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