Cremona's table of elliptic curves

2717 = 11 · 13 · 19

Field	Data	Notes
Atkin-Lehner	11+ 13- 19-	Signs for the Atkin-Lehner involutions
Class	2717c	Isogeny class
Conductor	2717	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	504	Modular degree for the optimal curve
Δ	2717 = 11 · 13 · 19	Discriminant
Eigenvalues	0 -2  0 -1 11+ 13-  0 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-793,8336]	[a1,a2,a3,a4,a6]
Generators	[-54:923:8]	Generators of the group modulo torsion
j	55219290112000/2717	j-invariant
L	1.7572720376652	L(r)(E,1)/r!
Ω	3.3981763236542	Real period
R	4.6540987967275	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	43472u1 24453k1 67925d1 29887e1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 2717c1

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	0	-1	+	-	0	-	-3	3	5	11	12	-10	0	-12	15	8	-4	0	11	-1	-15	9	-10

---

Quadratic twists for elliptic curve 2717c1

-4	-3	5	-11	13	-19
43472u1	24453k1	67925d1	29887e1	35321c1	51623b1

---

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