Cremona's table of elliptic curves

1650 = 2 · 3 · 5² · 11

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 11+	Signs for the Atkin-Lehner involutions
Class	1650a	Isogeny class
Conductor	1650	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	61256250000 = 24 · 34 · 58 · 112	Discriminant
Eigenvalues	2+ 3+ 5+  0 11+  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1875,28125]	[a1,a2,a3,a4,a6]
Generators	[-6:201:1]	Generators of the group modulo torsion
j	46694890801/3920400	j-invariant
L	1.8615790068002	L(r)(E,1)/r!
Ω	1.0817510997647	Real period
R	0.86044701373778	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	13200cg2 52800cp2 4950bi2 330b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1650a2

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
+	+	+	0	+	2	-2	-4	0	-2	0	2	2	12	-8	-6	-12	6	-4	0	6	-16	-4	10	-2

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Quadratic twists for elliptic curve 1650a2

-4	8	-3	5	-7	-11
13200cg2	52800cp2	4950bi2	330b2	80850cb2	18150bw2

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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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