Cremona's table of elliptic curves

15470 = 2 · 5 · 7 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2- 5+ 7+ 13- 17+	Signs for the Atkin-Lehner involutions
Class	15470k	Isogeny class
Conductor	15470	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	5760	Modular degree for the optimal curve
Δ	-158412800 = -1 · 212 · 52 · 7 · 13 · 17	Discriminant
Eigenvalues	2-  1 5+ 7+ -1 13- 17+  1	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,59,-575]	[a1,a2,a3,a4,a6]
Generators	[18:71:1]	Generators of the group modulo torsion
j	22689222191/158412800	j-invariant
L	7.6824861064109	L(r)(E,1)/r!
Ω	0.90703098441677	Real period
R	0.35291361956389	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	123760be1 77350m1 108290bk1	Quadratic twists by: -4 5 -7

Hecke Eigenvalues for elliptic curve 15470k1

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	+	+	-1	-	+	1	8	-8	10	-7	-8	5	-9	7	-4	6	-2	0	-2	-8	15	5	-12

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Quadratic twists for elliptic curve 15470k1

-4	5	-7
123760be1	77350m1	108290bk1

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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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