Cremona's table of elliptic curves

16400 = 2⁴ · 5² · 41

Field	Data	Notes
Atkin-Lehner	2+ 5+ 41+	Signs for the Atkin-Lehner involutions
Class	16400b	Isogeny class
Conductor	16400	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-53792000000 = -1 · 211 · 56 · 412	Discriminant
Eigenvalues	2+  0 5+ -2  0  4  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,725,8250]	[a1,a2,a3,a4,a6]
Generators	[15:150:1]	Generators of the group modulo torsion
j	1317006/1681	j-invariant
L	4.2690073651665	L(r)(E,1)/r!
Ω	0.75261037277836	Real period
R	1.418066877489	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	8200f2 65600be2 656a2	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 16400b2

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

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Quadratic twists for elliptic curve 16400b2

-4	8	5
8200f2	65600be2	656a2

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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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