Cremona's table of elliptic curves

42720 = 2⁵ · 3 · 5 · 89

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 89+	Signs for the Atkin-Lehner involutions
Class	42720h	Isogeny class
Conductor	42720	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1642498560 = 29 · 34 · 5 · 892	Discriminant
Eigenvalues	2- 3+ 5- -2  4 -6  6  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-320,1140]	[a1,a2,a3,a4,a6]
Generators	[17:18:1]	Generators of the group modulo torsion
j	7100029448/3208005	j-invariant
L	5.3398554403321	L(r)(E,1)/r!
Ω	1.344426313499	Real period
R	1.9859234331828	Regulator
r	1	Rank of the group of rational points
S	1.0000000000003	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	42720l2 85440bi2 128160m2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 42720h2

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

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Quadratic twists for elliptic curve 42720h2

-4	8	-3
42720l2	85440bi2	128160m2

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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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