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	6650l	Isogeny class
Conductor	6650	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	40000	Modular degree for the optimal curve
Δ	-1039062500 = -1 · 22 · 59 · 7 · 19	Discriminant
Eigenvalues	2+  1 5- 7+  2  6 -3 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-723201,-236780952]	[a1,a2,a3,a4,a6]
Generators	[8015337:611435416:1331]	Generators of the group modulo torsion
j	-21417553667311829/532	j-invariant
L	3.5416606091986	L(r)(E,1)/r!
Ω	0.081856821400184	Real period
R	10.816632470628	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	53200dr1 59850ge1 6650bi1 46550bf1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6650l1

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	-	+	2	6	-3	-	1	0	-8	-3	-3	-9	2	1	-10	-8	2	-13	-9	0	6	10	12

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Quadratic twists for elliptic curve 6650l1

-4	-3	5	-7	-19
53200dr1	59850ge1	6650bi1	46550bf1	126350df1

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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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