Cremona's table of elliptic curves

897 = 3 · 13 · 23

Field	Data	Notes
Atkin-Lehner	3- 13- 23+	Signs for the Atkin-Lehner involutions
Class	897d	Isogeny class
Conductor	897	Conductor
∏ cp	240	Product of Tamagawa factors cp
Δ	5.5473114131091E+19	Discriminant
Eigenvalues	1 3-  0 -2 -6 13- -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1725581,-795628249]	[a1,a2,a3,a4,a6]
Generators	[-627:6631:1]	Generators of the group modulo torsion
j	568236858838659098439625/55473114131090524557	j-invariant
L	3.0756516640154	L(r)(E,1)/r!
Ω	0.13255106261377	Real period
R	0.3867253876062	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	14352t2 57408e2 2691g2 22425d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 897d2

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
1	-	0	-2	-6	-	-6	2	+	2	4	-8	2	0	0	-2	8	14	-10	-12	6	0	-18	4	0

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Quadratic twists for elliptic curve 897d2

-4	8	-3	5	-7	-11	13	-23
14352t2	57408e2	2691g2	22425d2	43953e2	108537p2	11661m2	20631g2

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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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