Cremona's table of elliptic curves

1335 = 3 · 5 · 89

Field	Data	Notes
Atkin-Lehner	3- 5- 89-	Signs for the Atkin-Lehner involutions
Class	1335b	Isogeny class
Conductor	1335	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	16040025 = 34 · 52 · 892	Discriminant
Eigenvalues	-1 3- 5-  0  4 -6 -6  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-150,-693]	[a1,a2,a3,a4,a6]
j	373403541601/16040025	j-invariant
L	1.3677689667045	L(r)(E,1)/r!
Ω	1.3677689667045	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	21360j2 85440c2 4005c2 6675e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1335b2

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	-	-	0	4	-6	-6	8	8	6	-4	2	-6	4	0	-2	0	14	12	0	-6	16	12	-	-6

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Quadratic twists for elliptic curve 1335b2

-4	8	-3	5	-7	89
21360j2	85440c2	4005c2	6675e2	65415e2	118815b2

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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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