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	2706l	Isogeny class
Conductor	2706	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	585884178 = 2 · 310 · 112 · 41	Discriminant
Eigenvalues	2- 3+  0 -2 11-  2 -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-493,-4255]	[a1,a2,a3,a4,a6]
Generators	[-90:77:8]	Generators of the group modulo torsion
j	13253162604625/585884178	j-invariant
L	3.9553351846692	L(r)(E,1)/r!
Ω	1.0159418100087	Real period
R	3.8932694232118	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	21648y2 86592z2 8118b2 67650bg2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2706l2

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	-2	-	2	-6	0	-4	2	-8	-2	+	10	6	2	10	-8	4	-6	-14	-10	-16	-16	2

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Quadratic twists for elliptic curve 2706l2

-4	8	-3	5	-11	41
21648y2	86592z2	8118b2	67650bg2	29766g2	110946bd2

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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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