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	8	Product of Tamagawa factors cp
Δ	23665225625 = 54 · 314 · 41	Discriminant
Eigenvalues	-1  0 5-  0  0  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-136687,-19416626]	[a1,a2,a3,a4,a6]
Generators	[437:1821:1]	Generators of the group modulo torsion
j	282424500044580783681/23665225625	j-invariant
L	2.6171319392588	L(r)(E,1)/r!
Ω	0.24829501603375	Real period
R	5.270206347805	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	101680ba4 57195d4 31775a4	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 6355d3

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 6355d3

-4	-3	5
101680ba4	57195d4	31775a4

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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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