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	120	Product of Tamagawa factors cp
deg	12480	Modular degree for the optimal curve
Δ	-1685064059634661407 = -1 · 312 · 1310 · 23	Discriminant
Eigenvalues	1 3-  0 -2 -6 13- -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,130884,-59725523]	[a1,a2,a3,a4,a6]
Generators	[2987:162774:1]	Generators of the group modulo torsion
j	247963729379947346375/1685064059634661407	j-invariant
L	3.0756516640154	L(r)(E,1)/r!
Ω	0.13255106261377	Real period
R	0.77345077521239	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	14352t1 57408e1 2691g1 22425d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 897d1

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

---

Quadratic twists for elliptic curve 897d1

-4	8	-3	5	-7	-11	13	-23
14352t1	57408e1	2691g1	22425d1	43953e1	108537p1	11661m1	20631g1

---

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