Cremona's table of elliptic curves

16240 = 2⁴ · 5 · 7 · 29

Field	Data	Notes
Atkin-Lehner	2- 5+ 7+ 29+	Signs for the Atkin-Lehner involutions
Class	16240k	Isogeny class
Conductor	16240	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-602828800 = -1 · 212 · 52 · 7 · 292	Discriminant
Eigenvalues	2- -2 5+ 7+  0 -2  0 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-96,1204]	[a1,a2,a3,a4,a6]
Generators	[-6:40:1] [2:32:1]	Generators of the group modulo torsion
j	-24137569/147175	j-invariant
L	4.8114905929223	L(r)(E,1)/r!
Ω	1.4055271854029	Real period
R	0.85581599610655	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1015a1 64960bs1 81200bm1 113680bm1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 16240k1

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

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Quadratic twists for elliptic curve 16240k1

-4	8	5	-7
1015a1	64960bs1	81200bm1	113680bm1

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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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