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	3696k	Isogeny class
Conductor	3696	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-7805952 = -1 · 210 · 32 · 7 · 112	Discriminant
Eigenvalues	2+ 3-  0 7+ 11-  2 -8  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-8,132]	[a1,a2,a3,a4,a6]
Generators	[-2:12:1]	Generators of the group modulo torsion
j	-62500/7623	j-invariant
L	4.1220123004167	L(r)(E,1)/r!
Ω	1.9189478810847	Real period
R	0.5370146241396	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	1848h1 14784bo1 11088i1 92400z1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3696k1

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	-8	6	-8	-6	-10	2	-8	4	-2	2	8	2	-4	4	-4	8	18	2	-14

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Quadratic twists for elliptic curve 3696k1

-4	8	-3	5	-7	-11
1848h1	14784bo1	11088i1	92400z1	25872i1	40656y1

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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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