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	2709b	Isogeny class
Conductor	2709	Conductor
∏ cp	36	Product of Tamagawa factors cp
Δ	-4971056090130963 = -1 · 312 · 76 · 433	Discriminant
Eigenvalues	0 3-  0 7-  3  5  3  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-853320,303419259]	[a1,a2,a3,a4,a6]
j	-94260981564964864000/6819006982347	j-invariant
L	1.6441910718853	L(r)(E,1)/r!
Ω	0.41104776797133	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	43344x2 903b2 67725m2 18963k2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2709b2

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	5	3	2	-9	-6	5	2	3	-	0	-9	0	8	5	6	2	8	9	6	17

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Quadratic twists for elliptic curve 2709b2

-4	-3	5	-7	-43
43344x2	903b2	67725m2	18963k2	116487h2

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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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