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	5304f	Isogeny class
Conductor	5304	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	422773947648 = 28 · 32 · 133 · 174	Discriminant
Eigenvalues	2+ 3-  0 -4 -2 13+ 17-  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-11428,465392]	[a1,a2,a3,a4,a6]
Generators	[8:612:1]	Generators of the group modulo torsion
j	644811009586000/1651460733	j-invariant
L	4.0964081072594	L(r)(E,1)/r!
Ω	0.94618362202451	Real period
R	1.0823501939546	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	10608c2 42432n2 15912n2 68952bc2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 5304f2

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

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Quadratic twists for elliptic curve 5304f2

-4	8	-3	13	17
10608c2	42432n2	15912n2	68952bc2	90168d2

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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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