Cremona's table of elliptic curves

6695 = 5 · 13 · 103

Field	Data	Notes
Atkin-Lehner	5- 13+ 103-	Signs for the Atkin-Lehner involutions
Class	6695a	Isogeny class
Conductor	6695	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	608	Modular degree for the optimal curve
Δ	-87035 = -1 · 5 · 132 · 103	Discriminant
Eigenvalues	1 -1 5- -2  0 13+  0  7	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-52,-169]	[a1,a2,a3,a4,a6]
Generators	[26:117:1]	Generators of the group modulo torsion
j	-16022066761/87035	j-invariant
L	3.7915770380219	L(r)(E,1)/r!
Ω	0.88643233721717	Real period
R	2.1386725635061	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	107120p1 60255b1 33475b1 87035c1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 6695a1

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	-1	-	-2	0	+	0	7	4	-5	2	6	9	1	-13	3	5	7	-7	-14	1	-5	-12	-4	-14

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Quadratic twists for elliptic curve 6695a1

-4	-3	5	13
107120p1	60255b1	33475b1	87035c1

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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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