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	1067328900000000 = 28 · 36 · 58 · 114	Discriminant
Eigenvalues	2+ 3- 5+  0 11- -6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-25626,147148]	[a1,a2,a3,a4,a6]
Generators	[-118:1296:1]	Generators of the group modulo torsion
j	119102750067601/68309049600	j-invariant
L	2.4907858868082	L(r)(E,1)/r!
Ω	0.41992482284923	Real period
R	0.49429202388894	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	13200bi2 52800f2 4950be2 330c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1650h2

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 1650h2

-4	8	-3	5	-7	-11
13200bi2	52800f2	4950be2	330c2	80850w2	18150cp2

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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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