Cremona's table of elliptic curves

8736 = 2⁵ · 3 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7+ 13-	Signs for the Atkin-Lehner involutions
Class	8736d	Isogeny class
Conductor	8736	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	2763790848 = 29 · 33 · 7 · 134	Discriminant
Eigenvalues	2+ 3+  2 7+ -4 13-  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2072,-35532]	[a1,a2,a3,a4,a6]
j	1922350562504/5398029	j-invariant
L	1.4154285406421	L(r)(E,1)/r!
Ω	0.70771427032107	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	8736k3 17472co3 26208bm4 61152s4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8736d2

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	+	-4	-	6	-4	-8	-6	0	10	-10	8	0	10	0	-2	-4	12	14	0	16	-10	-2

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Quadratic twists for elliptic curve 8736d2

-4	8	-3	-7	13
8736k3	17472co3	26208bm4	61152s4	113568ca4

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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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