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	8050q	Isogeny class
Conductor	8050	Conductor
∏ cp	56	Product of Tamagawa factors cp
deg	32256	Modular degree for the optimal curve
Δ	-592480000000000 = -1 · 214 · 510 · 7 · 232	Discriminant
Eigenvalues	2-  0 5+ 7-  0 -4 -4 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-22255,-1727753]	[a1,a2,a3,a4,a6]
j	-78013216986489/37918720000	j-invariant
L	2.6742010133602	L(r)(E,1)/r!
Ω	0.19101435809716	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	64400ba1 72450bo1 1610a1 56350bm1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8050q1

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	+	-	0	-4	-4	-2	-	10	-6	6	-2	4	10	10	0	-10	12	4	10	8	-2	0	16

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Quadratic twists for elliptic curve 8050q1

-4	-3	5	-7
64400ba1	72450bo1	1610a1	56350bm1

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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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