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	8050r	Isogeny class
Conductor	8050	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	40320	Modular degree for the optimal curve
Δ	-7828162250781250 = -1 · 2 · 58 · 77 · 233	Discriminant
Eigenvalues	2-  0 5- 7+  4 -3 -1  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,6695,4249947]	[a1,a2,a3,a4,a6]
Generators	[7902:245695:8]	Generators of the group modulo torsion
j	84972077055/20040095362	j-invariant
L	6.024511496293	L(r)(E,1)/r!
Ω	0.32180067212138	Real period
R	6.2404173537801	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	64400ck1 72450bz1 8050j1 56350bu1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8050r1

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	-3	-1	0	+	0	-4	11	-10	-2	11	1	-8	-8	0	-4	-4	-11	-13	1	-7

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Quadratic twists for elliptic curve 8050r1

-4	-3	5	-7
64400ck1	72450bz1	8050j1	56350bu1

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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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