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	1650b	Isogeny class
Conductor	1650	Conductor
∏ cp	20	Product of Tamagawa factors cp
Δ	30197062500 = 22 · 3 · 56 · 115	Discriminant
Eigenvalues	2+ 3+ 5+  2 11- -4  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-251625,-48687375]	[a1,a2,a3,a4,a6]
j	112763292123580561/1932612	j-invariant
L	1.0658126922822	L(r)(E,1)/r!
Ω	0.21316253845643	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13200cf3 52800ce3 4950bf3 66c3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1650b3

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

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Quadratic twists for elliptic curve 1650b3

-4	8	-3	5	-7	-11
13200cf3	52800ce3	4950bf3	66c3	80850cp3	18150ca3

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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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