Cremona's table of elliptic curves

5655 = 3 · 5 · 13 · 29

Field	Data	Notes
Atkin-Lehner	3+ 5+ 13+ 29+	Signs for the Atkin-Lehner involutions
Class	5655a	Isogeny class
Conductor	5655	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	160777305 = 38 · 5 · 132 · 29	Discriminant
Eigenvalues	1 3+ 5+  2 -6 13+  2  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-483,-4248]	[a1,a2,a3,a4,a6]
Generators	[312:5352:1]	Generators of the group modulo torsion
j	12501706118329/160777305	j-invariant
L	3.6546789607408	L(r)(E,1)/r!
Ω	1.0189048549568	Real period
R	3.5868697091406	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	90480br1 16965q1 28275j1 73515d1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5655a1

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
1	+	+	2	-6	+	2	6	2	+	10	-2	2	12	-12	2	-4	2	-10	-16	-10	-14	14	-14	6

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Quadratic twists for elliptic curve 5655a1

-4	-3	5	13
90480br1	16965q1	28275j1	73515d1

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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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