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	4284f	Isogeny class
Conductor	4284	Conductor
∏ cp	84	Product of Tamagawa factors cp
deg	241920	Modular degree for the optimal curve
Δ	-7.385796132138E+19	Discriminant
Eigenvalues	2- 3-  3 7+  5  1 17-  3	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-22144296,-40111047772]	[a1,a2,a3,a4,a6]
j	-6434900743458429657088/395758108932291	j-invariant
L	2.9230199066929	L(r)(E,1)/r!
Ω	0.034797856032059	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	17136br1 68544bt1 1428b1 107100bo1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4284f1

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	+	5	1	-	3	5	2	0	2	-7	3	-12	-8	8	6	-8	0	-2	12	-10	0	12

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Quadratic twists for elliptic curve 4284f1

-4	8	-3	5	-7	17
17136br1	68544bt1	1428b1	107100bo1	29988bh1	72828x1

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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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