Cremona's table of elliptic curves

85176 = 2³ · 3² · 7 · 13²

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 13+	Signs for the Atkin-Lehner involutions
Class	85176bc	Isogeny class
Conductor	85176	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	397252095641856 = 28 · 38 · 72 · 136	Discriminant
Eigenvalues	2+ 3-  2 7-  0 13+ -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-18759,-241670]	[a1,a2,a3,a4,a6]
Generators	[-590:6885:8]	Generators of the group modulo torsion
j	810448/441	j-invariant
L	8.3639224912599	L(r)(E,1)/r!
Ω	0.43524846368223	Real period
R	4.8041079910894	Regulator
r	1	Rank of the group of rational points
S	1.0000000001577	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	28392bc2 504f2	Quadratic twists by: -3 13

Hecke Eigenvalues for elliptic curve 85176bc2

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	-	0	+	-6	4	4	-6	8	10	-10	12	-8	-6	4	-10	-12	4	-2	8	4	6	-10

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Quadratic twists for elliptic curve 85176bc2

-3	13
28392bc2	504f2

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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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