Cremona's table of elliptic curves

5695 = 5 · 17 · 67

Field	Data	Notes
Atkin-Lehner	5+ 17+ 67-	Signs for the Atkin-Lehner involutions
Class	5695a	Isogeny class
Conductor	5695	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	544	Modular degree for the optimal curve
Δ	-28475 = -1 · 52 · 17 · 67	Discriminant
Eigenvalues	-2 -1 5+  0 -1 -6 17+  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-6,12]	[a1,a2,a3,a4,a6]
Generators	[-2:3:1] [1:2:1]	Generators of the group modulo torsion
j	-28094464/28475	j-invariant
L	2.2629123501063	L(r)(E,1)/r!
Ω	3.4002706761823	Real period
R	0.33275473713856	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	91120h1 51255f1 28475e1 96815l1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 5695a1

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	-1	+	0	-1	-6	+	1	-4	-6	5	-8	-7	-10	0	-12	-3	-5	-	6	-10	11	11	5	2

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Quadratic twists for elliptic curve 5695a1

-4	-3	5	17
91120h1	51255f1	28475e1	96815l1

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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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