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	32	Product of Tamagawa factors cp
Δ	874266624 = 214 · 32 · 72 · 112	Discriminant
Eigenvalues	2- 3- -2 7+ 11+  2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-264,756]	[a1,a2,a3,a4,a6]
Generators	[-4:42:1]	Generators of the group modulo torsion
j	498677257/213444	j-invariant
L	3.6593547853021	L(r)(E,1)/r!
Ω	1.4251577567193	Real period
R	1.2838420055776	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	462c2 14784bu2 11088bm2 92400ed2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3696u2

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 3696u2

-4	8	-3	5	-7	-11
462c2	14784bu2	11088bm2	92400ed2	25872bm2	40656dj2

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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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