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	5355i	Isogeny class
Conductor	5355	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	-433755 = -1 · 36 · 5 · 7 · 17	Discriminant
Eigenvalues	-2 3- 5+ 7-  2 -1 17+  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-3,-32]	[a1,a2,a3,a4,a6]
Generators	[4:4:1]	Generators of the group modulo torsion
j	-4096/595	j-invariant
L	1.9515772422422	L(r)(E,1)/r!
Ω	1.3233077284871	Real period
R	0.73738602149379	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	85680do1 595c1 26775bh1 37485bw1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5355i1

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
-2	-	+	-	2	-1	+	2	1	-2	-5	-1	3	4	-1	-6	-6	-5	-6	-16	4	4	15	-14	-4

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Quadratic twists for elliptic curve 5355i1

-4	-3	5	-7	17
85680do1	595c1	26775bh1	37485bw1	91035bk1

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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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