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	4389b	Isogeny class
Conductor	4389	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	208	Modular degree for the optimal curve
Δ	4389 = 3 · 7 · 11 · 19	Discriminant
Eigenvalues	0 3+  1 7- 11+  0 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-5,5]	[a1,a2,a3,a4,a6]
Generators	[1:0:1]	Generators of the group modulo torsion
j	16777216/4389	j-invariant
L	2.7824320190232	L(r)(E,1)/r!
Ω	4.0827324668426	Real period
R	0.68151220821358	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	70224ci1 13167n1 109725bn1 30723w1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4389b1

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	-	+	0	-6	-	6	0	7	-6	-3	-10	-1	9	12	-9	8	3	6	-5	-4	-14	7

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Quadratic twists for elliptic curve 4389b1

-4	-3	5	-7	-11	-19
70224ci1	13167n1	109725bn1	30723w1	48279c1	83391q1

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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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