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	3696w	Isogeny class
Conductor	3696	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	10709766144 = 212 · 32 · 74 · 112	Discriminant
Eigenvalues	2- 3- -2 7+ 11-  6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-624,-3564]	[a1,a2,a3,a4,a6]
j	6570725617/2614689	j-invariant
L	1.9768467175414	L(r)(E,1)/r!
Ω	0.98842335877069	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	231a2 14784br2 11088bh2 92400ev2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3696w2

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	+	-	6	2	-4	0	-2	-8	6	10	4	8	6	-4	-10	12	0	2	-16	-4	18	2

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Quadratic twists for elliptic curve 3696w2

-4	8	-3	5	-7	-11
231a2	14784br2	11088bh2	92400ev2	25872bx2	40656dk2

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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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