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	6	Product of Tamagawa factors cp
deg	1728	Modular degree for the optimal curve
Δ	-270937359 = -1 · 33 · 7 · 11 · 194	Discriminant
Eigenvalues	-1 3-  2 7- 11+  2  2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-77,-840]	[a1,a2,a3,a4,a6]
Generators	[37:199:1]	Generators of the group modulo torsion
j	-50529889873/270937359	j-invariant
L	3.3122976209623	L(r)(E,1)/r!
Ω	0.72493434091882	Real period
R	3.0460667805806	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	70224bo1 13167j1 109725a1 30723i1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4389f1

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 4389f1

-4	-3	5	-7	-11	-19
70224bo1	13167j1	109725a1	30723i1	48279o1	83391h1

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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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