Cremona's table of elliptic curves

8236 = 2² · 29 · 71

Field	Data	Notes
Atkin-Lehner	2- 29+ 71+	Signs for the Atkin-Lehner involutions
Class	8236a	Isogeny class
Conductor	8236	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	20016	Modular degree for the optimal curve
Δ	9916247806544 = 24 · 293 · 714	Discriminant
Eigenvalues	2-  2 -2 -4 -2 -6  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-6449,131714]	[a1,a2,a3,a4,a6]
j	1854164242481152/619765487909	j-invariant
L	1.0022520217982	L(r)(E,1)/r!
Ω	0.66816801453215	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	32944e1 74124d1	Quadratic twists by: -4 -3

Hecke Eigenvalues for elliptic curve 8236a1

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	-4	-2	-6	6	2	-4	+	-2	-6	6	2	-6	-6	8	6	4	+	10	10	16	-6	6

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Quadratic twists for elliptic curve 8236a1

-4	-3
32944e1	74124d1

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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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