Cremona's table of elliptic curves

4216 = 2³ · 17 · 31

Field	Data	Notes
Atkin-Lehner	2- 17- 31+	Signs for the Atkin-Lehner involutions
Class	4216f	Isogeny class
Conductor	4216	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2368	Modular degree for the optimal curve
Δ	-41426416 = -1 · 24 · 174 · 31	Discriminant
Eigenvalues	2-  2 -3  5 -6 -6 17-  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,68,201]	[a1,a2,a3,a4,a6]
Generators	[12:51:1]	Generators of the group modulo torsion
j	2141549312/2589151	j-invariant
L	4.5220460935596	L(r)(E,1)/r!
Ω	1.3623806060382	Real period
R	0.41490297145284	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	8432f1 33728g1 37944c1 105400d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4216f1

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	-3	5	-6	-6	-	5	6	0	+	-2	-5	0	-8	-4	-9	-2	-4	-13	10	-12	6	-16	-11

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Quadratic twists for elliptic curve 4216f1

-4	8	-3	5	17
8432f1	33728g1	37944c1	105400d1	71672i1

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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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