Cremona's table of elliptic curves

2679 = 3 · 19 · 47

Field	Data	Notes
Atkin-Lehner	3+ 19- 47-	Signs for the Atkin-Lehner involutions
Class	2679c	Isogeny class
Conductor	2679	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	3024	Modular degree for the optimal curve
Δ	59701222989 = 33 · 196 · 47	Discriminant
Eigenvalues	2 3+ -3  1  3  0  0 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-1082,-6685]	[a1,a2,a3,a4,a6]
Generators	[-70:357:8]	Generators of the group modulo torsion
j	140218983313408/59701222989	j-invariant
L	4.7228502492589	L(r)(E,1)/r!
Ω	0.86483722149323	Real period
R	0.91016169129577	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	42864d1 8037d1 66975j1 50901m1	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 2679c1

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
2	+	-3	1	3	0	0	-	1	-1	-6	-9	-2	-6	-	-10	0	14	-8	-12	2	-13	-2	-10	3

---

Quadratic twists for elliptic curve 2679c1

-4	-3	5	-19	-47
42864d1	8037d1	66975j1	50901m1	125913a1

---

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