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	8463k	Isogeny class
Conductor	8463	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2048	Modular degree for the optimal curve
Δ	330057 = 32 · 7 · 132 · 31	Discriminant
Eigenvalues	-1 3-  0 7- -2 13+ -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-763,-8176]	[a1,a2,a3,a4,a6]
j	49128431640625/330057	j-invariant
L	0.90837595700209	L(r)(E,1)/r!
Ω	0.90837595700209	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	25389l1 59241l1 110019q1	Quadratic twists by: -3 -7 13

Hecke Eigenvalues for elliptic curve 8463k1

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
-1	-	0	-	-2	+	-6	0	-6	-8	-	-2	4	8	-2	-12	10	-2	12	12	2	8	12	-2	6

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Quadratic twists for elliptic curve 8463k1

-3	-7	13
25389l1	59241l1	110019q1

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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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