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	897b	Isogeny class
Conductor	897	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	160	Modular degree for the optimal curve
Δ	-5912127 = -1 · 32 · 134 · 23	Discriminant
Eigenvalues	-1 3+  2  4  0 13-  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-52,164]	[a1,a2,a3,a4,a6]
j	-15568817473/5912127	j-invariant
L	1.1256932605428	L(r)(E,1)/r!
Ω	2.2513865210855	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	14352bk1 57408bd1 2691d1 22425m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 897b1

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	4	0	-	2	0	+	-2	8	-6	2	4	-8	6	-4	14	8	8	2	16	0	-10	-2

---

Quadratic twists for elliptic curve 897b1

-4	8	-3	5	-7	-11	13	-23
14352bk1	57408bd1	2691d1	22425m1	43953u1	108537c1	11661a1	20631d1

---

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