Cremona's table of elliptic curves

3504 = 2⁴ · 3 · 73

Field	Data	Notes
Atkin-Lehner	2- 3+ 73-	Signs for the Atkin-Lehner involutions
Class	3504r	Isogeny class
Conductor	3504	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	-4780240896 = -1 · 212 · 3 · 733	Discriminant
Eigenvalues	2- 3+ -3  4  0 -4  3  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-437,4989]	[a1,a2,a3,a4,a6]
Generators	[-20:73:1]	Generators of the group modulo torsion
j	-2258403328/1167051	j-invariant
L	2.7446232284096	L(r)(E,1)/r!
Ω	1.2758900028376	Real period
R	0.7170480272086	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	219b2 14016cd2 10512x2 87600cg2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3504r2

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	4	0	-4	3	1	-6	-6	10	-7	0	-2	3	9	9	-1	13	-12	-	-11	-15	-18	5

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Quadratic twists for elliptic curve 3504r2

-4	8	-3	5
219b2	14016cd2	10512x2	87600cg2

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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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