Cremona's table of elliptic curves

6355 = 5 · 31 · 41

Field	Data	Notes
Atkin-Lehner	5- 31+ 41-	Signs for the Atkin-Lehner involutions
Class	6355d	Isogeny class
Conductor	6355	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	-54749119375 = -1 · 54 · 31 · 414	Discriminant
Eigenvalues	-1  0 5-  0  0  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-157,-11244]	[a1,a2,a3,a4,a6]
Generators	[10521:1073859:1]	Generators of the group modulo torsion
j	-425428681761/54749119375	j-invariant
L	2.6171319392588	L(r)(E,1)/r!
Ω	0.4965900320675	Real period
R	5.270206347805	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	101680ba1 57195d1 31775a1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 6355d1

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	0	-	0	0	2	6	-4	0	-6	+	-2	-	4	-8	10	4	-10	4	-8	10	-4	4	-2	-6

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Quadratic twists for elliptic curve 6355d1

-4	-3	5
101680ba1	57195d1	31775a1

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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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