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	3496f	Isogeny class
Conductor	3496	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	894976 = 211 · 19 · 23	Discriminant
Eigenvalues	2+  1  3 -2 -1 -2 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-24,-16]	[a1,a2,a3,a4,a6]
Generators	[-5:2:1]	Generators of the group modulo torsion
j	778034/437	j-invariant
L	4.3539999987046	L(r)(E,1)/r!
Ω	2.3120380650949	Real period
R	1.8831869874625	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6992c1 27968g1 31464l1 87400k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3496f1

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
+	1	3	-2	-1	-2	-6	-	-	-5	-2	10	0	5	-11	-14	5	-2	10	0	-17	-9	-5	-1	-1

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Quadratic twists for elliptic curve 3496f1

-4	8	-3	5	-19	-23
6992c1	27968g1	31464l1	87400k1	66424n1	80408d1

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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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