Cremona's table of elliptic curves

31584 = 2⁵ · 3 · 7 · 47

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7- 47+	Signs for the Atkin-Lehner involutions
Class	31584d	Isogeny class
Conductor	31584	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	570028032 = 212 · 32 · 7 · 472	Discriminant
Eigenvalues	2+ 3+  0 7-  6  4 -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-273,-1215]	[a1,a2,a3,a4,a6]
j	551368000/139167	j-invariant
L	2.3918977258531	L(r)(E,1)/r!
Ω	1.1959488629271	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	31584j2 63168dg1 94752bk2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 31584d2

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

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Quadratic twists for elliptic curve 31584d2

-4	8	-3
31584j2	63168dg1	94752bk2

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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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