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	3496b	Isogeny class
Conductor	3496	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2112	Modular degree for the optimal curve
Δ	-2573056 = -1 · 28 · 19 · 232	Discriminant
Eigenvalues	2+  0 -3 -5  3 -6 -5 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1484,22004]	[a1,a2,a3,a4,a6]
Generators	[-2:158:1] [2:138:1]	Generators of the group modulo torsion
j	-1411839894528/10051	j-invariant
L	3.4700886963543	L(r)(E,1)/r!
Ω	2.2967052678887	Real period
R	0.1888623207814	Regulator
r	2	Rank of the group of rational points
S	0.99999999999991	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6992f1 27968p1 31464i1 87400g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3496b1

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	-3	-5	3	-6	-5	+	-	-6	-4	-10	-4	3	-9	0	-12	5	-2	2	13	-2	0	-14	10

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Quadratic twists for elliptic curve 3496b1

-4	8	-3	5	-19	-23
6992f1	27968p1	31464i1	87400g1	66424l1	80408f1

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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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