Cremona's table of elliptic curves

8050 = 2 · 5² · 7 · 23

Field	Data	Notes
Atkin-Lehner	2+ 5+ 7+ 23+	Signs for the Atkin-Lehner involutions
Class	8050c	Isogeny class
Conductor	8050	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	120376586914062500 = 22 · 518 · 73 · 23	Discriminant
Eigenvalues	2+  2 5+ 7+ -6  4 -6  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-264525,-49744375]	[a1,a2,a3,a4,a6]
Generators	[-2316100:8729675:6859]	Generators of the group modulo torsion
j	131010595463836369/7704101562500	j-invariant
L	4.1006765553099	L(r)(E,1)/r!
Ω	0.21128829815616	Real period
R	9.7039840613398	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	64400ca3 72450ea3 1610e3 56350i3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8050c3

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

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Quadratic twists for elliptic curve 8050c3

-4	-3	5	-7
64400ca3	72450ea3	1610e3	56350i3

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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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