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	3696n	Isogeny class
Conductor	3696	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	-89600963493888 = -1 · 214 · 32 · 73 · 116	Discriminant
Eigenvalues	2- 3+  0 7+ 11-  2  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-13168,743104]	[a1,a2,a3,a4,a6]
Generators	[106:-726:1]	Generators of the group modulo torsion
j	-61653281712625/21875235228	j-invariant
L	2.9985944629888	L(r)(E,1)/r!
Ω	0.56885607798039	Real period
R	0.43927257102164	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	462g3 14784cc3 11088bf3 92400he3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3696n3

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

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Quadratic twists for elliptic curve 3696n3

-4	8	-3	5	-7	-11
462g3	14784cc3	11088bf3	92400he3	25872ct3	40656bq3

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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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