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	4389f	Isogeny class
Conductor	4389	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	1560329001 = 36 · 72 · 112 · 192	Discriminant
Eigenvalues	-1 3-  2 7- 11+  2  2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1882,-31525]	[a1,a2,a3,a4,a6]
Generators	[-25:20:1]	Generators of the group modulo torsion
j	737219801902753/1560329001	j-invariant
L	3.3122976209623	L(r)(E,1)/r!
Ω	0.72493434091882	Real period
R	1.5230333902903	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	70224bo2 13167j2 109725a2 30723i2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4389f2

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
-1	-	2	-	+	2	2	+	-8	-10	-8	-2	-2	-12	-8	10	-12	-6	-4	12	6	-12	16	6	6

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Quadratic twists for elliptic curve 4389f2

-4	-3	5	-7	-11	-19
70224bo2	13167j2	109725a2	30723i2	48279o2	83391h2

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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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