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	16	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	386358336 = 26 · 36 · 72 · 132	Discriminant
Eigenvalues	2+ 3+  2 7+ -4 13-  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-182,0]	[a1,a2,a3,a4,a6]
j	10474708672/6036849	j-invariant
L	1.4154285406421	L(r)(E,1)/r!
Ω	1.4154285406421	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	8736k1 17472co2 26208bm1 61152s1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8736d1

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 8736d1

-4	8	-3	-7	13
8736k1	17472co2	26208bm1	61152s1	113568ca1

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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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