Cremona's table of elliptic curves

5355 = 3² · 5 · 7 · 17

Field	Data	Notes
Atkin-Lehner	3+ 5- 7+ 17-	Signs for the Atkin-Lehner involutions
Class	5355b	Isogeny class
Conductor	5355	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-112455 = -1 · 33 · 5 · 72 · 17	Discriminant
Eigenvalues	-1 3+ 5- 7+  0  0 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-2,-16]	[a1,a2,a3,a4,a6]
Generators	[4:3:1]	Generators of the group modulo torsion
j	-19683/4165	j-invariant
L	2.5449958153138	L(r)(E,1)/r!
Ω	1.4864073574691	Real period
R	1.7121792370882	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	85680dh1 5355a1 26775c1 37485b1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5355b1

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

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Quadratic twists for elliptic curve 5355b1

-4	-3	5	-7	17
85680dh1	5355a1	26775c1	37485b1	91035a1

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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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