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	2	Product of Tamagawa factors cp
deg	360	Modular degree for the optimal curve
Δ	-507812500 = -1 · 22 · 510 · 13	Discriminant
Eigenvalues	2-  2 5+  1  3 13+ -3 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-638,6031]	[a1,a2,a3,a4,a6]
j	-2941225/52	j-invariant
L	3.3093399101418	L(r)(E,1)/r!
Ω	1.6546699550709	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	5200r1 20800bd1 5850h1 650g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 650i1

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 650i1

-4	8	-3	5	-7	-11	13
5200r1	20800bd1	5850h1	650g1	31850cc1	78650s1	8450e1

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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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