Cremona's table of elliptic curves

4214 = 2 · 7² · 43

Field	Data	Notes
Atkin-Lehner	2- 7- 43+	Signs for the Atkin-Lehner involutions
Class	4214d	Isogeny class
Conductor	4214	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	4032	Modular degree for the optimal curve
Δ	-888425011712 = -1 · 29 · 79 · 43	Discriminant
Eigenvalues	2-  1  0 7- -1  2 -4 -5	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2108,-58864]	[a1,a2,a3,a4,a6]
Generators	[200:2644:1]	Generators of the group modulo torsion
j	-25672375/22016	j-invariant
L	5.969876429027	L(r)(E,1)/r!
Ω	0.3400294832387	Real period
R	0.97538542379805	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	33712q1 37926j1 105350p1 4214e1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4214d1

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
-	1	0	-	-1	2	-4	-5	-6	-1	-5	-3	2	+	0	-4	0	14	-3	1	6	-10	14	13	-8

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Quadratic twists for elliptic curve 4214d1

-4	-3	5	-7
33712q1	37926j1	105350p1	4214e1

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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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