Cremona's table of elliptic curves

42504 = 2³ · 3 · 7 · 11 · 23

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 11+ 23-	Signs for the Atkin-Lehner involutions
Class	42504q	Isogeny class
Conductor	42504	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	66194709504 = 210 · 3 · 7 · 11 · 234	Discriminant
Eigenvalues	2- 3+ -2 7- 11+ -6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-5104,-138116]	[a1,a2,a3,a4,a6]
Generators	[-42:20:1] [-39:10:1]	Generators of the group modulo torsion
j	14362857077188/64643271	j-invariant
L	7.1715854260102	L(r)(E,1)/r!
Ω	0.56497913801454	Real period
R	6.3467701225319	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	85008q3 127512s3	Quadratic twists by: -4 -3

Hecke Eigenvalues for elliptic curve 42504q3

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	-	+	-6	-2	4	-	-6	-8	-2	2	-4	-8	2	-12	2	0	0	-10	-16	12	2	-2

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Quadratic twists for elliptic curve 42504q3

-4	-3
85008q3	127512s3

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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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