Cremona's table of elliptic curves

10850 = 2 · 5² · 7 · 31

Field	Data	Notes
Atkin-Lehner	2+ 5+ 7+ 31+	Signs for the Atkin-Lehner involutions
Class	10850c	Isogeny class
Conductor	10850	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1107994752200000000 = 29 · 58 · 78 · 312	Discriminant
Eigenvalues	2+  2 5+ 7+ -2 -4  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1667900,826850000]	[a1,a2,a3,a4,a6]
Generators	[242137:344443:343]	Generators of the group modulo torsion
j	32840829570040809409/70911664140800	j-invariant
L	4.4542463301273	L(r)(E,1)/r!
Ω	0.27583471690685	Real period
R	8.0741220323465	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	86800cf2 97650cy2 2170l2 75950bh2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 10850c2

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	6	4	4	-8	+	-4	6	10	-8	12	-8	-4	-4	-16	-6	-12	6	-6	18

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Quadratic twists for elliptic curve 10850c2

-4	-3	5	-7
86800cf2	97650cy2	2170l2	75950bh2

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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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