Cremona's table of elliptic curves

60840 = 2³ · 3² · 5 · 13²

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 13+	Signs for the Atkin-Lehner involutions
Class	60840p	Isogeny class
Conductor	60840	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	299520	Modular degree for the optimal curve
Δ	237867078243600 = 24 · 36 · 52 · 138	Discriminant
Eigenvalues	2+ 3- 5+ -3 -5 13+ -5 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-85683,-9625057]	[a1,a2,a3,a4,a6]
Generators	[-169:169:1] [-166:155:1]	Generators of the group modulo torsion
j	7311616/25	j-invariant
L	8.4217134211304	L(r)(E,1)/r!
Ω	0.27910343337968	Real period
R	2.514513860553	Regulator
r	2	Rank of the group of rational points
S	0.9999999999996	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	121680u1 6760k1 60840bx1	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 60840p1

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
+	-	+	-3	-5	+	-5	-1	1	9	-4	-3	1	-3	8	-10	-3	7	-9	-7	10	-16	-12	-15	-7

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Quadratic twists for elliptic curve 60840p1

-4	-3	13
121680u1	6760k1	60840bx1

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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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