Cremona's table of elliptic curves

2989 = 7² · 61

Field	Data	Notes
Atkin-Lehner	7- 61-	Signs for the Atkin-Lehner involutions
Class	2989b	Isogeny class
Conductor	2989	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1056	Modular degree for the optimal curve
Δ	-50236123 = -1 · 77 · 61	Discriminant
Eigenvalues	0 -2 -4 7- -2 -2 -5  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-65,375]	[a1,a2,a3,a4,a6]
Generators	[-5:24:1]	Generators of the group modulo torsion
j	-262144/427	j-invariant
L	1.1327009119605	L(r)(E,1)/r!
Ω	1.7957357894392	Real period
R	0.1576931470963	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	47824x1 26901r1 74725l1 427a1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2989b1

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	-2	-4	-	-2	-2	-5	8	-6	2	-1	4	0	8	8	-12	-1	-	6	6	10	-14	2	-10	2

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Quadratic twists for elliptic curve 2989b1

-4	-3	5	-7
47824x1	26901r1	74725l1	427a1

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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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