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	2706i	Isogeny class
Conductor	2706	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-3661218 = -1 · 2 · 32 · 112 · 412	Discriminant
Eigenvalues	2+ 3- -4  0 11- -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-18,-98]	[a1,a2,a3,a4,a6]
Generators	[14:42:1]	Generators of the group modulo torsion
j	-594823321/3661218	j-invariant
L	2.303036942245	L(r)(E,1)/r!
Ω	1.0423544662985	Real period
R	1.1047282938323	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	21648o2 86592d2 8118n2 67650bv2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2706i2

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
+	-	-4	0	-	-2	-2	4	6	0	-4	2	+	8	-12	-10	-4	-4	12	0	-6	4	4	-6	-18

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Quadratic twists for elliptic curve 2706i2

-4	8	-3	5	-11	41
21648o2	86592d2	8118n2	67650bv2	29766bw2	110946c2

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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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