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	3504q	Isogeny class
Conductor	3504	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	127298469888 = 215 · 36 · 732	Discriminant
Eigenvalues	2- 3+  0  4  6 -4 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-497688,-134974224]	[a1,a2,a3,a4,a6]
Generators	[220418:103482610:1]	Generators of the group modulo torsion
j	3328404840479049625/31078728	j-invariant
L	3.4032279367981	L(r)(E,1)/r!
Ω	0.17974639538918	Real period
R	9.4667487752105	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	438d2 14016ca2 10512t2 87600ch2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3504q2

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	4	6	-4	-6	-8	0	0	-8	2	-6	-2	0	-12	-6	-10	4	0	-	16	-6	6	14

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Quadratic twists for elliptic curve 3504q2

-4	8	-3	5
438d2	14016ca2	10512t2	87600ch2

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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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