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	5355p	Isogeny class
Conductor	5355	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	4495158945703125 = 39 · 58 · 7 · 174	Discriminant
Eigenvalues	1 3- 5- 7-  0 -2 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-42939,1161148]	[a1,a2,a3,a4,a6]
Generators	[-28:1544:1]	Generators of the group modulo torsion
j	12010404962647729/6166198828125	j-invariant
L	4.9735355072901	L(r)(E,1)/r!
Ω	0.38417245335713	Real period
R	0.80913133278889	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	85680fe3 1785c4 26775w3 37485r3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5355p3

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

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Quadratic twists for elliptic curve 5355p3

-4	-3	5	-7	17
85680fe3	1785c4	26775w3	37485r3	91035g3

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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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