Cremona's table of elliptic curves

2684 = 2² · 11 · 61

Field	Data	Notes
Atkin-Lehner	2- 11+ 61-	Signs for the Atkin-Lehner involutions
Class	2684b	Isogeny class
Conductor	2684	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	180	Modular degree for the optimal curve
Δ	-10736 = -1 · 24 · 11 · 61	Discriminant
Eigenvalues	2- -1 -2  1 11+  2 -3  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-34,89]	[a1,a2,a3,a4,a6]
Generators	[4:-1:1]	Generators of the group modulo torsion
j	-279738112/671	j-invariant
L	2.4643016264668	L(r)(E,1)/r!
Ω	4.0620226108869	Real period
R	0.20222287125811	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	10736j1 42944i1 24156g1 67100b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2684b1

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
-	-1	-2	1	+	2	-3	6	8	2	-2	-6	2	-8	3	6	-6	-	-10	-6	-10	3	-8	6	-11

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Quadratic twists for elliptic curve 2684b1

-4	8	-3	5	-11
10736j1	42944i1	24156g1	67100b1	29524g1

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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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