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	4	Product of Tamagawa factors cp
deg	512	Modular degree for the optimal curve
Δ	-137904 = -1 · 24 · 3 · 132 · 17	Discriminant
Eigenvalues	2+ 3+  2 -2  4 13- 17- -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,13,0]	[a1,a2,a3,a4,a6]
Generators	[4:10:1]	Generators of the group modulo torsion
j	14047232/8619	j-invariant
L	3.6743828518935	L(r)(E,1)/r!
Ω	2.0199283295572	Real period
R	1.8190659530474	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	10608j1 42432u1 15912q1 68952w1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 5304c1

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 5304c1

-4	8	-3	13	17
10608j1	42432u1	15912q1	68952w1	90168p1

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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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