Cremona's table of elliptic curves

6314 = 2 · 7 · 11 · 41

Field	Data	Notes
Atkin-Lehner	2+ 7- 11+ 41-	Signs for the Atkin-Lehner involutions
Class	6314d	Isogeny class
Conductor	6314	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-76668325888 = -1 · 212 · 73 · 113 · 41	Discriminant
Eigenvalues	2+ -2  0 7- 11+  2 -6 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,909,-8050]	[a1,a2,a3,a4,a6]
Generators	[31:208:1]	Generators of the group modulo torsion
j	83195910236375/76668325888	j-invariant
L	2.0084467400109	L(r)(E,1)/r!
Ω	0.59578736764395	Real period
R	0.56184662769686	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	50512f2 56826bf2 44198h2 69454n2	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6314d2

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
+	-2	0	-	+	2	-6	-1	6	3	5	-7	-	-1	6	0	-12	-1	-7	15	11	-10	12	-9	-13

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Quadratic twists for elliptic curve 6314d2

-4	-3	-7	-11
50512f2	56826bf2	44198h2	69454n2

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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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