Cremona's table of elliptic curves

8710 = 2 · 5 · 13 · 67

Field	Data	Notes
Atkin-Lehner	2- 5- 13- 67+	Signs for the Atkin-Lehner involutions
Class	8710k	Isogeny class
Conductor	8710	Conductor
∏ cp	380	Product of Tamagawa factors cp
deg	3693600	Modular degree for the optimal curve
Δ	-5.2429761004639E+24	Discriminant
Eigenvalues	2-  0 5-  3  3 13-  2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1694011867,-26836111752341]	[a1,a2,a3,a4,a6]
j	-537617079035035624542262006188801/5242976100463867187500000	j-invariant
L	4.4711968376467	L(r)(E,1)/r!
Ω	0.011766307467491	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	69680bi1 78390n1 43550a1 113230c1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 8710k1

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	-	3	3	-	2	-2	-4	4	8	-3	-2	-6	2	0	14	13	+	9	4	10	-9	-11	7

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Quadratic twists for elliptic curve 8710k1

-4	-3	5	13
69680bi1	78390n1	43550a1	113230c1

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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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