Cremona's table of elliptic curves

8080 = 2⁴ · 5 · 101

Field	Data	Notes
Atkin-Lehner	2- 5- 101+	Signs for the Atkin-Lehner involutions
Class	8080i	Isogeny class
Conductor	8080	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	1010000 = 24 · 54 · 101	Discriminant
Eigenvalues	2-  2 5-  2 -2 -2 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-25,0]	[a1,a2,a3,a4,a6]
Generators	[90:255:8]	Generators of the group modulo torsion
j	112377856/63125	j-invariant
L	6.3246477028129	L(r)(E,1)/r!
Ω	2.2889404417256	Real period
R	2.7631333640314	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	2020b1 32320r1 72720bp1 40400q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8080i1

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	-	2	-2	-2	-2	-8	0	-6	-4	-6	2	12	8	14	6	-6	-14	-4	-10	-12	-6	-14	2

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Quadratic twists for elliptic curve 8080i1

-4	8	-3	5
2020b1	32320r1	72720bp1	40400q1

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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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