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	4284d	Isogeny class
Conductor	4284	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	873936 = 24 · 33 · 7 · 172	Discriminant
Eigenvalues	2- 3+  2 7- -2  2 17- -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-24,5]	[a1,a2,a3,a4,a6]
j	3538944/2023	j-invariant
L	2.4059991793864	L(r)(E,1)/r!
Ω	2.4059991793864	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17136q1 68544v1 4284c1 107100a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4284d1

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	-	-2	2	-	-6	6	-6	4	2	6	12	8	4	12	0	4	2	-16	0	-4	-10	12

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Quadratic twists for elliptic curve 4284d1

-4	8	-3	5	-7	17
17136q1	68544v1	4284c1	107100a1	29988i1	72828b1

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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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