Cremona's table of elliptic curves

2726 = 2 · 29 · 47

Field	Data	Notes
Atkin-Lehner	2+ 29+ 47+	Signs for the Atkin-Lehner involutions
Class	2726a	Isogeny class
Conductor	2726	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	2200	Modular degree for the optimal curve
Δ	45734690816 = 225 · 29 · 47	Discriminant
Eigenvalues	2+  0 -1  4  0 -1  4 -7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1670,-23756]	[a1,a2,a3,a4,a6]
Generators	[-21:52:1]	Generators of the group modulo torsion
j	515251659466809/45734690816	j-invariant
L	2.4824449210649	L(r)(E,1)/r!
Ω	0.75104047380908	Real period
R	3.3053410670061	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	21808d1 87232f1 24534u1 68150o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2726a1

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	-1	4	0	-1	4	-7	3	+	0	-11	5	-1	+	-6	-3	7	-4	-12	-7	5	-4	0	2

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Quadratic twists for elliptic curve 2726a1

-4	8	-3	5	29	-47
21808d1	87232f1	24534u1	68150o1	79054f1	128122b1

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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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