Cremona's table of elliptic curves

320 = 2⁶ · 5

Field	Data	Notes
Atkin-Lehner	2+ 5+	Signs for the Atkin-Lehner involutions
Class	320b	Isogeny class
Conductor	320	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	327680 = 216 · 5	Discriminant
Eigenvalues	2+  0 5+ -4 -4  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-428,-3408]	[a1,a2,a3,a4,a6]
Generators	[24:12:1]	Generators of the group modulo torsion
j	132304644/5	j-invariant
L	1.5161085153166	L(r)(E,1)/r!
Ω	1.0496381260349	Real period
R	2.8888213522577	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	320a3 40a2 2880t3 1600a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 320b3

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

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Quadratic twists for elliptic curve 320b3

-4	8	-3	5	-7	-11	13	17	-19
320a3	40a2	2880t3	1600a3	15680bm3	38720f4	54080bf4	92480bs4	115520j4

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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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