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	18	Product of Tamagawa factors cp
deg	7056	Modular degree for the optimal curve
Δ	-28821108096 = -1 · 27 · 33 · 112 · 413	Discriminant
Eigenvalues	2+ 3- -3 -4 11+  5  3  5	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-7245,236872]	[a1,a2,a3,a4,a6]
Generators	[-38:695:1]	Generators of the group modulo torsion
j	-42048713138244553/28821108096	j-invariant
L	2.2301681082559	L(r)(E,1)/r!
Ω	1.1689509664675	Real period
R	0.95391858693409	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	21648x1 86592y1 8118o1 67650bt1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2706f1

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 2706f1

-4	8	-3	5	-11	41
21648x1	86592y1	8118o1	67650bt1	29766bm1	110946j1

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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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