Cremona's table of elliptic curves

6650 = 2 · 5² · 7 · 19

Field	Data	Notes
Atkin-Lehner	2+ 5- 7+ 19+	Signs for the Atkin-Lehner involutions
Class	6650i	Isogeny class
Conductor	6650	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	7200	Modular degree for the optimal curve
Δ	43331732500 = 22 · 54 · 7 · 195	Discriminant
Eigenvalues	2+  1 5- 7+ -3  1  2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-5001,-136152]	[a1,a2,a3,a4,a6]
j	22125312720025/69330772	j-invariant
L	1.1356841261645	L(r)(E,1)/r!
Ω	0.56784206308225	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	53200eb1 59850ft1 6650y2 46550bm1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6650i1

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
+	1	-	+	-3	1	2	+	-4	0	7	-8	7	1	2	6	-5	-8	12	-8	6	-10	16	-5	7

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Quadratic twists for elliptic curve 6650i1

-4	-3	5	-7	-19
53200eb1	59850ft1	6650y2	46550bm1	126350dg1

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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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