Cremona's table of elliptic curves

63840 = 2⁵ · 3 · 5 · 7 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 7+ 19-	Signs for the Atkin-Lehner involutions
Class	63840k	Isogeny class
Conductor	63840	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	32768	Modular degree for the optimal curve
Δ	12481358400 = 26 · 32 · 52 · 74 · 192	Discriminant
Eigenvalues	2+ 3+ 5- 7+  0 -2  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-610,2392]	[a1,a2,a3,a4,a6]
Generators	[-2:60:1]	Generators of the group modulo torsion
j	392866508224/195021225	j-invariant
L	5.3904024215228	L(r)(E,1)/r!
Ω	1.121726750687	Real period
R	2.4027252707784	Regulator
r	1	Rank of the group of rational points
S	0.99999999999172	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	63840bz1 127680bw2	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 63840k1

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

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Quadratic twists for elliptic curve 63840k1

-4	8
63840bz1	127680bw2

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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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