Cremona's table of elliptic curves

2706 = 2 · 3 · 11 · 41

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11+ 41+	Signs for the Atkin-Lehner involutions
Class	2706a	Isogeny class
Conductor	2706	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-14644872 = -1 · 23 · 32 · 112 · 412	Discriminant
Eigenvalues	2+ 3+  0 -4 11+  6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,15,189]	[a1,a2,a3,a4,a6]
Generators	[3:15:1]	Generators of the group modulo torsion
j	335702375/14644872	j-invariant
L	1.8640034611953	L(r)(E,1)/r!
Ω	1.6828633170324	Real period
R	0.55381903043745	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	21648be2 86592bk2 8118r2 67650cj2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2706a2

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
+	+	0	-4	+	6	-2	-4	6	4	4	2	+	-4	8	6	-8	0	-4	-12	-14	0	4	6	-2

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Quadratic twists for elliptic curve 2706a2

-4	8	-3	5	-11	41
21648be2	86592bk2	8118r2	67650cj2	29766bi2	110946n2

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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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