Cremona's table of elliptic curves

42439 = 31 · 37²

Field	Data	Notes
Atkin-Lehner	31+ 37+	Signs for the Atkin-Lehner involutions
Class	42439b	Isogeny class
Conductor	42439	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	7.7808851834393E+25	Discriminant
Eigenvalues	2 -1  4  3 -3 -4  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-401884096,-3071670174971]	[a1,a2,a3,a4,a6]
Generators	[-493277677106214001707567739267740:-7133810562558701010015868439133607:42162241736487123050754024000]	Generators of the group modulo torsion
j	2797794606468551643136/30326246618289637	j-invariant
L	13.068157324293	L(r)(E,1)/r!
Ω	0.033741062609266	Real period
R	48.413403112209	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	1147b2	Quadratic twists by: 37

Hecke Eigenvalues for elliptic curve 42439b2

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	-1	4	3	-3	-4	2	0	-4	0	+	+	7	-4	3	-1	10	8	-12	-3	-11	0	-1	-10	2

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Quadratic twists for elliptic curve 42439b2

37
1147b2

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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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