Cremona's table of elliptic curves

4686 = 2 · 3 · 11 · 71

Field	Data	Notes
Atkin-Lehner	2- 3+ 11+ 71-	Signs for the Atkin-Lehner involutions
Class	4686b	Isogeny class
Conductor	4686	Conductor
∏ cp	240	Product of Tamagawa factors cp
deg	248640	Modular degree for the optimal curve
Δ	-2.1719903722415E+20	Discriminant
Eigenvalues	2- 3+  2  2 11+ -6 -4  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,155738,-708607069]	[a1,a2,a3,a4,a6]
Generators	[1633:61663:1]	Generators of the group modulo torsion
j	417741207055683511967/217199037224152203264	j-invariant
L	5.374372853728	L(r)(E,1)/r!
Ω	0.082963905306	Real period
R	1.0796608545016	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	37488ba1 14058d1 117150u1 51546b1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4686b1

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	+	-6	-4	4	-8	-6	-6	-6	-12	-8	12	8	0	-2	-14	-	6	8	4	-2	-2

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Quadratic twists for elliptic curve 4686b1

-4	-3	5	-11
37488ba1	14058d1	117150u1	51546b1

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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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