Cremona's table of elliptic curves

40896 = 2⁶ · 3² · 71

Field	Data	Notes
Atkin-Lehner	2+ 3- 71-	Signs for the Atkin-Lehner involutions
Class	40896ba	Isogeny class
Conductor	40896	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-1014012692361216 = -1 · 212 · 320 · 71	Discriminant
Eigenvalues	2+ 3- -2  2  0  2  4  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-22836,-2027680]	[a1,a2,a3,a4,a6]
Generators	[89270:2324808:125]	Generators of the group modulo torsion
j	-441058644928/339590799	j-invariant
L	5.8459628835196	L(r)(E,1)/r!
Ω	0.18793329057121	Real period
R	7.7766462580306	Regulator
r	1	Rank of the group of rational points
S	0.99999999999996	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	40896r2 20448f1 13632b2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 40896ba2

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	2	0	2	4	0	0	10	-2	6	4	-4	-12	-12	4	-2	2	-	-10	-16	4	18	-10

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Quadratic twists for elliptic curve 40896ba2

-4	8	-3
40896r2	20448f1	13632b2

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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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