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	5355r	Isogeny class
Conductor	5355	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	71134464515625 = 38 · 56 · 74 · 172	Discriminant
Eigenvalues	-1 3- 5- 7-  0 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-10427,-54574]	[a1,a2,a3,a4,a6]
Generators	[-84:514:1]	Generators of the group modulo torsion
j	171963096231529/97578140625	j-invariant
L	2.6935556022212	L(r)(E,1)/r!
Ω	0.51005183567842	Real period
R	0.44007873543521	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	85680fg2 1785j2 26775t2 37485u2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5355r2

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	-2	-	-4	8	-2	-8	2	-6	-8	8	-2	-4	-2	-8	4	-2	-8	12	-10	-10

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Quadratic twists for elliptic curve 5355r2

-4	-3	5	-7	17
85680fg2	1785j2	26775t2	37485u2	91035j2

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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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