Cremona's table of elliptic curves

5270 = 2 · 5 · 17 · 31

Field	Data	Notes
Atkin-Lehner	2+ 5+ 17+ 31-	Signs for the Atkin-Lehner involutions
Class	5270b	Isogeny class
Conductor	5270	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	2112	Modular degree for the optimal curve
Δ	40515760 = 24 · 5 · 17 · 313	Discriminant
Eigenvalues	2+  1 5+  2 -6  5 17+  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-394,2956]	[a1,a2,a3,a4,a6]
j	6739487929369/40515760	j-invariant
L	1.36726009336	L(r)(E,1)/r!
Ω	2.05089014004	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	42160l1 47430bl1 26350p1 89590e1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 5270b1

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	+	2	-6	5	+	2	3	-3	-	2	-6	8	9	3	6	2	-7	-15	2	-10	12	0	14

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Quadratic twists for elliptic curve 5270b1

-4	-3	5	17
42160l1	47430bl1	26350p1	89590e1

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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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