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	2684a	Isogeny class
Conductor	2684	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	228	Modular degree for the optimal curve
Δ	-10736 = -1 · 24 · 11 · 61	Discriminant
Eigenvalues	2-  3 -2  1 11+  4  1  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1,5]	[a1,a2,a3,a4,a6]
j	-6912/671	j-invariant
L	3.3312040331055	L(r)(E,1)/r!
Ω	3.3312040331055	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	10736i1 42944n1 24156f1 67100a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2684a1

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	-2	1	+	4	1	0	6	-6	2	6	10	-4	3	6	6	+	8	-12	-4	15	-2	-18	5

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Quadratic twists for elliptic curve 2684a1

-4	8	-3	5	-11
10736i1	42944n1	24156f1	67100a1	29524k1

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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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