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	3496a	Isogeny class
Conductor	3496	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	-70276592 = -1 · 24 · 192 · 233	Discriminant
Eigenvalues	2+  1  2  0  0 -7  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,48,-367]	[a1,a2,a3,a4,a6]
Generators	[7:19:1]	Generators of the group modulo torsion
j	748596992/4392287	j-invariant
L	4.3131713993105	L(r)(E,1)/r!
Ω	0.97548187349769	Real period
R	1.1053950658881	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	6992h1 27968k1 31464j1 87400j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3496a1

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	2	0	0	-7	2	+	+	-1	-7	2	9	-10	3	4	-4	-8	-12	9	-3	8	4	-12	-2

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Quadratic twists for elliptic curve 3496a1

-4	8	-3	5	-19	-23
6992h1	27968k1	31464j1	87400j1	66424j1	80408g1

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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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