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	8463d	Isogeny class
Conductor	8463	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	27648	Modular degree for the optimal curve
Δ	15542054073 = 32 · 73 · 132 · 313	Discriminant
Eigenvalues	1 3+  2 7- -2 13-  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-212894,37720263]	[a1,a2,a3,a4,a6]
Generators	[254:209:1]	Generators of the group modulo torsion
j	1067129596696048382953/15542054073	j-invariant
L	4.9884664130905	L(r)(E,1)/r!
Ω	0.88265636112123	Real period
R	1.8838839337028	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25389n1 59241s1 110019f1	Quadratic twists by: -3 -7 13

Hecke Eigenvalues for elliptic curve 8463d1

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

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Quadratic twists for elliptic curve 8463d1

-3	-7	13
25389n1	59241s1	110019f1

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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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