Cremona's table of elliptic curves

8463 = 3 · 7 · 13 · 31

Field	Data	Notes
Atkin-Lehner	3- 7+ 13- 31-	Signs for the Atkin-Lehner involutions
Class	8463j	Isogeny class
Conductor	8463	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	-21895651323 = -1 · 38 · 72 · 133 · 31	Discriminant
Eigenvalues	-2 3- -2 7+ -5 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-8104,278206]	[a1,a2,a3,a4,a6]
Generators	[-103:175:1] [5908864:21323858:148877]	Generators of the group modulo torsion
j	-58867500778688512/21895651323	j-invariant
L	3.2330926280902	L(r)(E,1)/r!
Ω	1.185585490171	Real period
R	0.056812517508832	Regulator
r	2	Rank of the group of rational points
S	0.99999999999986	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	25389i1 59241f1 110019w1	Quadratic twists by: -3 -7 13

Hecke Eigenvalues for elliptic curve 8463j1

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	+	-5	-	-6	-4	-4	-8	-	-5	0	-8	-2	-4	-4	-10	6	-6	13	-8	-16	9	4

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Quadratic twists for elliptic curve 8463j1

-3	-7	13
25389i1	59241f1	110019w1

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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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