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	8050b	Isogeny class
Conductor	8050	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	7471470336050000000 = 27 · 58 · 710 · 232	Discriminant
Eigenvalues	2+  2 5+ 7+ -2  4  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-628000,-139536000]	[a1,a2,a3,a4,a6]
Generators	[-37131315:194427895:59319]	Generators of the group modulo torsion
j	1753007192038126081/478174101507200	j-invariant
L	4.2810279137222	L(r)(E,1)/r!
Ω	0.17306680069408	Real period
R	12.368137321985	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	64400bz2 72450dv2 1610g2 56350g2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8050b2

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	4	2	-4	+	-2	-4	8	-2	-10	12	4	10	-14	-10	-16	-6	-4	-12	-6	14

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Quadratic twists for elliptic curve 8050b2

-4	-3	5	-7
64400bz2	72450dv2	1610g2	56350g2

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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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