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	2706f	Isogeny class
Conductor	2706	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-456973621395456 = -1 · 221 · 3 · 116 · 41	Discriminant
Eigenvalues	2+ 3- -3 -4 11+  5  3  5	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,6900,1005130]	[a1,a2,a3,a4,a6]
Generators	[-10:7987:8]	Generators of the group modulo torsion
j	36338036700986567/456973621395456	j-invariant
L	2.2301681082559	L(r)(E,1)/r!
Ω	0.38965032215585	Real period
R	2.8617557608023	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	21648x2 86592y2 8118o2 67650bt2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2706f2

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
+	-	-3	-4	+	5	3	5	0	-6	5	-10	-	8	-12	12	3	-10	-7	-9	-1	-16	-15	-3	14

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Quadratic twists for elliptic curve 2706f2

-4	8	-3	5	-11	41
21648x2	86592y2	8118o2	67650bt2	29766bm2	110946j2

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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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