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	4284c	Isogeny class
Conductor	4284	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	637099344 = 24 · 39 · 7 · 172	Discriminant
Eigenvalues	2- 3+ -2 7-  2  2 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-216,-135]	[a1,a2,a3,a4,a6]
Generators	[-12:27:1]	Generators of the group modulo torsion
j	3538944/2023	j-invariant
L	3.421769727648	L(r)(E,1)/r!
Ω	1.3490574163415	Real period
R	0.84547173115072	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	17136n1 68544p1 4284d1 107100c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4284c1

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 4284c1

-4	8	-3	5	-7	17
17136n1	68544p1	4284d1	107100c1	29988n1	72828a1

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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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