Cremona's table of elliptic curves

2678 = 2 · 13 · 103

Field	Data	Notes
Atkin-Lehner	2- 13- 103+	Signs for the Atkin-Lehner involutions
Class	2678l	Isogeny class
Conductor	2678	Conductor
∏ cp	15	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	305945432 = 23 · 135 · 103	Discriminant
Eigenvalues	2-  0 -2 -1  5 13- -3 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-241,1225]	[a1,a2,a3,a4,a6]
Generators	[13:6:1]	Generators of the group modulo torsion
j	1541999809377/305945432	j-invariant
L	4.175689358551	L(r)(E,1)/r!
Ω	1.6339807971988	Real period
R	0.17036876507197	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	21424s1 85696c1 24102m1 66950e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2678l1

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
-	0	-2	-1	5	-	-3	-2	0	-6	6	-10	-10	6	0	5	0	-8	1	-4	-11	6	-18	6	-10

---

Quadratic twists for elliptic curve 2678l1

-4	8	-3	5	13
21424s1	85696c1	24102m1	66950e1	34814a1

---

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