Cremona's table of elliptic curves

2709 = 3² · 7 · 43

Field	Data	Notes
Atkin-Lehner	3- 7+ 43-	Signs for the Atkin-Lehner involutions
Class	2709a	Isogeny class
Conductor	2709	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-13824027 = -1 · 38 · 72 · 43	Discriminant
Eigenvalues	0 3-  0 7+  3  1 -1 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,60,0]	[a1,a2,a3,a4,a6]
Generators	[8:31:1]	Generators of the group modulo torsion
j	32768000/18963	j-invariant
L	2.7283870607835	L(r)(E,1)/r!
Ω	1.3325987474582	Real period
R	0.51185457475244	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	43344bj1 903a1 67725v1 18963j1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2709a1

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	-	0	+	3	1	-1	-6	-1	10	-7	2	7	-	-8	7	8	-8	13	-10	-6	-8	-11	-2	-11

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Quadratic twists for elliptic curve 2709a1

-4	-3	5	-7	-43
43344bj1	903a1	67725v1	18963j1	116487k1

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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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