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	5304i	Isogeny class
Conductor	5304	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	6619392 = 28 · 32 · 132 · 17	Discriminant
Eigenvalues	2- 3+ -4  2 -2 13+ 17-  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-820,9316]	[a1,a2,a3,a4,a6]
Generators	[4:78:1]	Generators of the group modulo torsion
j	238481570896/25857	j-invariant
L	2.5068184982824	L(r)(E,1)/r!
Ω	2.2769414219086	Real period
R	0.27523967834239	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	10608i2 42432bh2 15912d2 68952k2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 5304i2

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
-	+	-4	2	-2	+	-	0	0	-6	2	4	8	4	-4	2	4	6	-8	-6	4	12	0	2	8

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Quadratic twists for elliptic curve 5304i2

-4	8	-3	13	17
10608i2	42432bh2	15912d2	68952k2	90168bb2

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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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