Cremona's table of elliptic curves

6670 = 2 · 5 · 23 · 29

Field	Data	Notes
Atkin-Lehner	2+ 5- 23+ 29-	Signs for the Atkin-Lehner involutions
Class	6670c	Isogeny class
Conductor	6670	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	5040	Modular degree for the optimal curve
Δ	8975152000 = 27 · 53 · 23 · 293	Discriminant
Eigenvalues	2+  1 5-  2 -3 -1  6 -7	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1338,18156]	[a1,a2,a3,a4,a6]
Generators	[-30:192:1]	Generators of the group modulo torsion
j	264621653112601/8975152000	j-invariant
L	3.804177184266	L(r)(E,1)/r!
Ω	1.2925302494517	Real period
R	2.9432016665603	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	53360r1 60030bj1 33350o1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 6670c1

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	-3	-1	6	-7	+	-	-4	5	-6	8	6	0	-3	-10	11	6	-7	-10	-12	-9	8

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Quadratic twists for elliptic curve 6670c1

-4	-3	5
53360r1	60030bj1	33350o1

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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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