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	897c	Isogeny class
Conductor	897	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	897 = 3 · 13 · 23	Discriminant
Eigenvalues	-1 3+ -2  0  0 13-  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-19,-40]	[a1,a2,a3,a4,a6]
Generators	[6:7:1]	Generators of the group modulo torsion
j	761048497/897	j-invariant
L	1.2516489191625	L(r)(E,1)/r!
Ω	2.2862457181884	Real period
R	2.1898764585187	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	14352be1 57408bh1 2691c1 22425l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 897c1

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

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Quadratic twists for elliptic curve 897c1

-4	8	-3	5	-7	-11	13	-23
14352be1	57408bh1	2691c1	22425l1	43953w1	108537g1	11661e1	20631c1

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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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