Cremona's table of elliptic curves

42600 = 2³ · 3 · 5² · 71

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 71-	Signs for the Atkin-Lehner involutions
Class	42600m	Isogeny class
Conductor	42600	Conductor
∏ cp	90	Product of Tamagawa factors cp
deg	158400	Modular degree for the optimal curve
Δ	543577331250000 = 24 · 35 · 58 · 713	Discriminant
Eigenvalues	2+ 3- 5- -2 -3 -6 -5 -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-31583,1835838]	[a1,a2,a3,a4,a6]
Generators	[58:-450:1] [49:639:1]	Generators of the group modulo torsion
j	557464975360/86972373	j-invariant
L	9.9170085106413	L(r)(E,1)/r!
Ω	0.49739424950478	Real period
R	0.22153248366119	Regulator
r	2	Rank of the group of rational points
S	0.99999999999982	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	85200o1 127800bq1 42600s1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 42600m1

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	-3	-6	-5	-5	1	-6	0	-3	-5	-7	8	1	9	0	-10	-	1	-11	0	-4	-10

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Quadratic twists for elliptic curve 42600m1

-4	-3	5
85200o1	127800bq1	42600s1

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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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