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	650i	Isogeny class
Conductor	650	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-1373125000000 = -1 · 26 · 510 · 133	Discriminant
Eigenvalues	2-  2 5+  1  3 13+ -3 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,2487,31031]	[a1,a2,a3,a4,a6]
j	174196775/140608	j-invariant
L	3.3093399101418	L(r)(E,1)/r!
Ω	0.55155665169029	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	5200r2 20800bd2 5850h2 650g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 650i2

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	+	1	3	+	-3	-4	6	-3	-1	-2	0	10	3	-3	-15	-13	13	0	10	-4	-15	6	4

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Quadratic twists for elliptic curve 650i2

-4	8	-3	5	-7	-11	13
5200r2	20800bd2	5850h2	650g2	31850cc2	78650s2	8450e2

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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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