Cremona's table of elliptic curves

13350 = 2 · 3 · 5² · 89

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 89+	Signs for the Atkin-Lehner involutions
Class	13350i	Isogeny class
Conductor	13350	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2112	Modular degree for the optimal curve
Δ	-2136000 = -1 · 26 · 3 · 53 · 89	Discriminant
Eigenvalues	2+ 3- 5-  0  2 -2 -2  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,14,68]	[a1,a2,a3,a4,a6]
Generators	[6:16:1]	Generators of the group modulo torsion
j	2685619/17088	j-invariant
L	4.3330470222726	L(r)(E,1)/r!
Ω	1.8899568588004	Real period
R	2.2926698046552	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	106800bk1 40050bl1 13350m1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 13350i1

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
+	-	-	0	2	-2	-2	2	6	-6	-4	6	-6	4	-12	10	-4	-12	-12	0	4	-16	8	+	-4

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Quadratic twists for elliptic curve 13350i1

-4	-3	5
106800bk1	40050bl1	13350m1

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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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