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
deg	59904	Modular degree for the optimal curve
Δ	53230625000000 = 26 · 510 · 7 · 233	Discriminant
Eigenvalues	2+  2 5+ 7+ -6  4 -6  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-46025,3765125]	[a1,a2,a3,a4,a6]
Generators	[-230:1615:1]	Generators of the group modulo torsion
j	690080604747409/3406760000	j-invariant
L	4.1006765553099	L(r)(E,1)/r!
Ω	0.63386489446847	Real period
R	3.2346613537799	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	64400ca1 72450ea1 1610e1 56350i1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8050c1

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 8050c1

-4	-3	5	-7
64400ca1	72450ea1	1610e1	56350i1

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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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