Cremona's table of elliptic curves

650 = 2 · 5² · 13

Field	Data	Notes
Atkin-Lehner	2- 5+ 13+	Signs for the Atkin-Lehner involutions
Class	650h	Isogeny class
Conductor	650	Conductor
∏ cp	9	Product of Tamagawa factors cp
Δ	-104000000 = -1 · 29 · 56 · 13	Discriminant
Eigenvalues	2- -1 5+  1  6 13+  3  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-11488,-478719]	[a1,a2,a3,a4,a6]
j	-10730978619193/6656	j-invariant
L	2.0751559917619	L(r)(E,1)/r!
Ω	0.23057288797355	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5200p3 20800v3 5850i3 26a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 650h3

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
-	-1	+	1	6	+	3	2	0	6	-4	7	0	1	-3	0	-6	8	-14	-3	-2	8	-12	-6	10

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Quadratic twists for elliptic curve 650h3

-4	8	-3	5	-7	-11	13
5200p3	20800v3	5850i3	26a2	31850bz3	78650p3	8450c3

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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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