Cremona's table of elliptic curves

5304 = 2³ · 3 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3+ 13- 17-	Signs for the Atkin-Lehner involutions
Class	5304c	Isogeny class
Conductor	5304	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	8656128 = 28 · 32 · 13 · 172	Discriminant
Eigenvalues	2+ 3+  2 -2  4 13- 17- -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-52,52]	[a1,a2,a3,a4,a6]
Generators	[-2:12:1]	Generators of the group modulo torsion
j	61918288/33813	j-invariant
L	3.6743828518935	L(r)(E,1)/r!
Ω	2.0199283295572	Real period
R	0.9095329765237	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	10608j2 42432u2 15912q2 68952w2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 5304c2

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

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Quadratic twists for elliptic curve 5304c2

-4	8	-3	13	17
10608j2	42432u2	15912q2	68952w2	90168p2

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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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