Cremona's table of elliptic curves

861 = 3 · 7 · 41

Field	Data	Notes
Atkin-Lehner	3+ 7- 41+	Signs for the Atkin-Lehner involutions
Class	861a	Isogeny class
Conductor	861	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	56	Modular degree for the optimal curve
Δ	-23247 = -1 · 34 · 7 · 41	Discriminant
Eigenvalues	-1 3+  2 7-  0  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,3,-6]	[a1,a2,a3,a4,a6]
j	2924207/23247	j-invariant
L	0.94298550013938	L(r)(E,1)/r!
Ω	1.8859710002788	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13776o1 55104bk1 2583e1 21525v1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 861a1

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

---

Quadratic twists for elliptic curve 861a1

-4	8	-3	5	-7	-11	41
13776o1	55104bk1	2583e1	21525v1	6027h1	104181e1	35301h1

---

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