Cremona's table of elliptic curves

3496 = 2³ · 19 · 23

Field	Data	Notes
Atkin-Lehner	2+ 19+ 23-	Signs for the Atkin-Lehner involutions
Class	3496c	Isogeny class
Conductor	3496	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	-132848 = -1 · 24 · 192 · 23	Discriminant
Eigenvalues	2+ -3  0 -2 -6 -3 -8 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,5,-17]	[a1,a2,a3,a4,a6]
Generators	[3:5:1] [7:19:1]	Generators of the group modulo torsion
j	864000/8303	j-invariant
L	2.7837360867011	L(r)(E,1)/r!
Ω	1.6230502872241	Real period
R	0.42878155233619	Regulator
r	2	Rank of the group of rational points
S	0.99999999999943	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6992g1 27968u1 31464g1 87400i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3496c1

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
+	-3	0	-2	-6	-3	-8	+	-	3	-7	8	-7	-6	-9	12	-12	-4	-2	5	-11	-8	-6	-8	-8

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Quadratic twists for elliptic curve 3496c1

-4	8	-3	5	-19	-23
6992g1	27968u1	31464g1	87400i1	66424o1	80408j1

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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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