Cremona's table of elliptic curves

2695 = 5 · 7² · 11

Field	Data	Notes
Atkin-Lehner	5+ 7- 11-	Signs for the Atkin-Lehner involutions
Class	2695c	Isogeny class
Conductor	2695	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	-301437326575 = -1 · 52 · 77 · 114	Discriminant
Eigenvalues	-1  0 5+ 7- 11-  6 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1798,-39028]	[a1,a2,a3,a4,a6]
Generators	[62:260:1]	Generators of the group modulo torsion
j	-5461074081/2562175	j-invariant
L	1.9204853927889	L(r)(E,1)/r!
Ω	0.3585278894594	Real period
R	2.6782928877369	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	43120be1 24255bn1 13475h1 385a1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2695c1

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	+	-	-	6	-6	4	-8	-10	4	6	10	4	4	6	0	6	4	0	-6	-8	-12	-10	-10

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Quadratic twists for elliptic curve 2695c1

-4	-3	5	-7	-11
43120be1	24255bn1	13475h1	385a1	29645d1

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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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