Cremona's table of elliptic curves

4418 = 2 · 47²

Field	Data	Notes
Atkin-Lehner	2- 47-	Signs for the Atkin-Lehner involutions
Class	4418a	Isogeny class
Conductor	4418	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	4416	Modular degree for the optimal curve
Δ	-2026492481852 = -1 · 22 · 477	Discriminant
Eigenvalues	2-  0  0  0 -2  4 -2  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,690,67961]	[a1,a2,a3,a4,a6]
Generators	[15606:681401:8]	Generators of the group modulo torsion
j	3375/188	j-invariant
L	5.2441423083841	L(r)(E,1)/r!
Ω	0.62987394064712	Real period
R	4.1628506673862	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	35344a1 39762c1 110450a1 94a1	Quadratic twists by: -4 -3 5 -47

Hecke Eigenvalues for elliptic curve 4418a1

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
-	0	0	0	-2	4	-2	2	-4	-4	-4	2	-6	-6	-	2	12	2	-2	8	14	-16	-16	-10	-14

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Quadratic twists for elliptic curve 4418a1

-4	-3	5	-47
35344a1	39762c1	110450a1	94a1

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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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