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	897f	Isogeny class
Conductor	897	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	557037 = 34 · 13 · 232	Discriminant
Eigenvalues	-1 3- -4  2  2 13- -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-65,-204]	[a1,a2,a3,a4,a6]
Generators	[-5:4:1]	Generators of the group modulo torsion
j	30400540561/557037	j-invariant
L	1.6264676608294	L(r)(E,1)/r!
Ω	1.6831372042242	Real period
R	0.48316550093105	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	14352x2 57408l2 2691f2 22425a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 897f2

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

---

Quadratic twists for elliptic curve 897f2

-4	8	-3	5	-7	-11	13	-23
14352x2	57408l2	2691f2	22425a2	43953h2	108537o2	11661k2	20631i2

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations