Cremona's table of elliptic curves

80 = 2⁴ · 5

Field	Data	Notes
Atkin-Lehner	2+ 5-	Signs for the Atkin-Lehner involutions
Class	80a	Isogeny class
Conductor	80	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-640000 = -1 · 210 · 54	Discriminant
Eigenvalues	2+  0 5-  4 -4 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,13,34]	[a1,a2,a3,a4,a6]
j	237276/625	j-invariant
L	1.0094529099892	L(r)(E,1)/r!
Ω	2.0189058199784	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	40a4 320a4 720d4 400a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 80a4

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 80a4

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37
40a4	320a4	720d4	400a4	3920d4	9680h4	13520a4	23120a3	28880h3	42320c3	67280g3	76880j3	109520a3

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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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