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	1650h	Isogeny class
Conductor	1650	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	10047556406250000 = 24 · 312 · 510 · 112	Discriminant
Eigenvalues	2+ 3- 5+  0 11- -6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-267626,-53092852]	[a1,a2,a3,a4,a6]
Generators	[-303:601:1]	Generators of the group modulo torsion
j	135670761487282321/643043610000	j-invariant
L	2.4907858868082	L(r)(E,1)/r!
Ω	0.20996241142462	Real period
R	0.98858404777787	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	13200bi4 52800f3 4950be4 330c3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1650h3

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	-	-6	-2	-4	0	-10	0	-6	2	-4	8	10	-4	-2	4	-8	-2	-8	12	-6	-18

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Quadratic twists for elliptic curve 1650h3

-4	8	-3	5	-7	-11
13200bi4	52800f3	4950be4	330c3	80850w3	18150cp4

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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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