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	2706b	Isogeny class
Conductor	2706	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	128128	Modular degree for the optimal curve
Δ	-1840836121344 = -1 · 28 · 32 · 117 · 41	Discriminant
Eigenvalues	2+ 3+  3  5 11+ -6  5 -1	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-9642336,11520467712]	[a1,a2,a3,a4,a6]
j	-99144942546405114122445577/1840836121344	j-invariant
L	1.7244874633657	L(r)(E,1)/r!
Ω	0.43112186584143	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	21648bh1 86592br1 8118p1 67650cn1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2706b1

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	5	+	-6	5	-1	-1	1	3	1	-	10	2	0	-11	10	14	-10	-6	12	0	6	4

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Quadratic twists for elliptic curve 2706b1

-4	8	-3	5	-11	41
21648bh1	86592br1	8118p1	67650cn1	29766bd1	110946p1

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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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