Cremona's table of elliptic curves

4284 = 2² · 3² · 7 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 17+	Signs for the Atkin-Lehner involutions
Class	4284g	Isogeny class
Conductor	4284	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	13824	Modular degree for the optimal curve
Δ	-59438820397824 = -1 · 28 · 39 · 74 · 173	Discriminant
Eigenvalues	2- 3-  3 7-  3 -1 17+  5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-26976,-1745228]	[a1,a2,a3,a4,a6]
j	-11632923639808/318495051	j-invariant
L	2.9753891737511	L(r)(E,1)/r!
Ω	0.18596182335944	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	17136ba1 68544cf1 1428e1 107100bf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4284g1

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
-	-	3	-	3	-1	+	5	3	6	-10	-4	9	-1	6	-6	6	8	-4	12	-10	-10	-6	-12	8

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Quadratic twists for elliptic curve 4284g1

-4	8	-3	5	-7	17
17136ba1	68544cf1	1428e1	107100bf1	29988bo1	72828r1

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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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