Cremona's table of elliptic curves

63168 = 2⁶ · 3 · 7 · 47

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 47+	Signs for the Atkin-Lehner involutions
Class	63168bo	Isogeny class
Conductor	63168	Conductor
∏ cp	108	Product of Tamagawa factors cp
deg	677376	Modular degree for the optimal curve
Δ	18786781955132352 = 26 · 318 · 73 · 472	Discriminant
Eigenvalues	2+ 3- -2 7-  4 -4  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-308824,-65829418]	[a1,a2,a3,a4,a6]
Generators	[-331:486:1]	Generators of the group modulo torsion
j	50895369988415092288/293543468048943	j-invariant
L	6.993141980452	L(r)(E,1)/r!
Ω	0.2025921055587	Real period
R	1.2784568175961	Regulator
r	1	Rank of the group of rational points
S	0.99999999997141	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	63168k1 31584e2	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 63168bo1

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	-4	0	4	-8	2	0	-2	10	-10	+	6	12	-14	14	6	-4	-4	-16	16	-18

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Quadratic twists for elliptic curve 63168bo1

-4	8
63168k1	31584e2

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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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