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	3696g	Isogeny class
Conductor	3696	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	99792 = 24 · 34 · 7 · 11	Discriminant
Eigenvalues	2+ 3+ -2 7- 11- -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2079,-35802]	[a1,a2,a3,a4,a6]
Generators	[8270:41808:125]	Generators of the group modulo torsion
j	62140690757632/6237	j-invariant
L	2.7369092524238	L(r)(E,1)/r!
Ω	0.70699855858762	Real period
R	7.7423333306121	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	1848j1 14784cl1 11088v1 92400by1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3696g1

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	-4	0	6	8	-10	-6	12	8	-10	-12	-2	4	0	-6	0	12	10	-14

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Quadratic twists for elliptic curve 3696g1

-4	8	-3	5	-7	-11
1848j1	14784cl1	11088v1	92400by1	25872w1	40656l1

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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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