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	2695a	Isogeny class
Conductor	2695	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-6470695 = -1 · 5 · 76 · 11	Discriminant
Eigenvalues	1  0 5+ 7- 11+ -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,40,-85]	[a1,a2,a3,a4,a6]
j	59319/55	j-invariant
L	1.301160423914	L(r)(E,1)/r!
Ω	1.301160423914	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	43120bo1 24255bv1 13475e1 55a4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2695a1

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	+	-	+	-2	-6	4	4	6	8	-2	-2	4	12	-2	-4	10	-16	8	-14	8	4	-10	-10

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Quadratic twists for elliptic curve 2695a1

-4	-3	5	-7	-11
43120bo1	24255bv1	13475e1	55a4	29645h1

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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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