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	1650d	Isogeny class
Conductor	1650	Conductor
∏ cp	30	Product of Tamagawa factors cp
deg	1200	Modular degree for the optimal curve
Δ	-1207882500 = -1 · 22 · 3 · 54 · 115	Discriminant
Eigenvalues	2+ 3+ 5- -3 11- -4  7  5	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,250,-600]	[a1,a2,a3,a4,a6]
Generators	[70:570:1]	Generators of the group modulo torsion
j	2747555975/1932612	j-invariant
L	1.7338529787553	L(r)(E,1)/r!
Ω	0.86718359040154	Real period
R	0.066646901453801	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13200cq1 52800dt1 4950br1 1650s2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1650d1

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
+	+	-	-3	-	-4	7	5	1	-10	2	7	-3	-4	-13	-4	-5	12	12	-3	-4	-15	-14	0	7

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Quadratic twists for elliptic curve 1650d1

-4	8	-3	5	-7	-11
13200cq1	52800dt1	4950br1	1650s2	80850dh1	18150ci1

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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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