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
deg	2016	Modular degree for the optimal curve
Δ	-84910672 = -1 · 24 · 7 · 11 · 413	Discriminant
Eigenvalues	2+ -2  0 7- 11+  2 -6 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-116,642]	[a1,a2,a3,a4,a6]
Generators	[5:11:1]	Generators of the group modulo torsion
j	-170492253625/84910672	j-invariant
L	2.0084467400109	L(r)(E,1)/r!
Ω	1.7873621029318	Real period
R	1.6855398830906	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	50512f1 56826bf1 44198h1 69454n1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6314d1

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 6314d1

-4	-3	-7	-11
50512f1	56826bf1	44198h1	69454n1

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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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