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	8	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-66957494448 = -1 · 24 · 3 · 136 · 172	Discriminant
Eigenvalues	2+ 3-  0 -4 -2 13+ 17-  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-443,12810]	[a1,a2,a3,a4,a6]
Generators	[6:102:1]	Generators of the group modulo torsion
j	-602275072000/4184843403	j-invariant
L	4.0964081072594	L(r)(E,1)/r!
Ω	0.94618362202451	Real period
R	2.1647003879091	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	10608c1 42432n1 15912n1 68952bc1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 5304f1

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 5304f1

-4	8	-3	13	17
10608c1	42432n1	15912n1	68952bc1	90168d1

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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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