Cremona's table of elliptic curves

26896 = 2⁴ · 41²

Field	Data	Notes
Atkin-Lehner	2- 41+	Signs for the Atkin-Lehner involutions
Class	26896c	Isogeny class
Conductor	26896	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	4516806656 = 216 · 413	Discriminant
Eigenvalues	2-  2  2 -2 -6 -4  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-55992,5118320]	[a1,a2,a3,a4,a6]
j	68769820673/16	j-invariant
L	2.1913276630261	L(r)(E,1)/r!
Ω	1.0956638315133	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3362c2 107584o2 26896d2	Quadratic twists by: -4 8 41

Hecke Eigenvalues for elliptic curve 26896c2

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

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Quadratic twists for elliptic curve 26896c2

-4	8	41
3362c2	107584o2	26896d2

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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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