Cremona's table of elliptic curves

4389 = 3 · 7 · 11 · 19

Field	Data	Notes
Atkin-Lehner	3- 7- 11+ 19+	Signs for the Atkin-Lehner involutions
Class	4389g	Isogeny class
Conductor	4389	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	2160	Modular degree for the optimal curve
Δ	39501 = 33 · 7 · 11 · 19	Discriminant
Eigenvalues	2 3- -1 7- 11+ -4 -4 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-1156,14749]	[a1,a2,a3,a4,a6]
Generators	[154:-1:8]	Generators of the group modulo torsion
j	170990840664064/39501	j-invariant
L	7.6128569836901	L(r)(E,1)/r!
Ω	2.8911980813781	Real period
R	0.87770499396356	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	70224bn1 13167l1 109725d1 30723j1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4389g1

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
2	-	-1	-	+	-4	-4	+	-2	-4	-5	4	-5	-12	13	-5	6	15	14	9	-6	3	-2	0	15

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Quadratic twists for elliptic curve 4389g1

-4	-3	5	-7	-11	-19
70224bn1	13167l1	109725d1	30723j1	48279t1	83391j1

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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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