Cremona's table of elliptic curves

3696 = 2⁴ · 3 · 7 · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 11+	Signs for the Atkin-Lehner involutions
Class	3696u	Isogeny class
Conductor	3696	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-15138816 = -1 · 216 · 3 · 7 · 11	Discriminant
Eigenvalues	2- 3- -2 7+ 11+  2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,56,116]	[a1,a2,a3,a4,a6]
Generators	[7:30:1]	Generators of the group modulo torsion
j	4657463/3696	j-invariant
L	3.6593547853021	L(r)(E,1)/r!
Ω	1.4251577567193	Real period
R	2.5676840111552	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	462c1 14784bu1 11088bm1 92400ed1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3696u1

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	-6	4	4	2	4	-2	-6	0	8	-14	-12	-14	-4	-12	6	0	0	-6	-14

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Quadratic twists for elliptic curve 3696u1

-4	8	-3	5	-7	-11
462c1	14784bu1	11088bm1	92400ed1	25872bm1	40656dj1

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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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