Cremona's table of elliptic curves

2704 = 2⁴ · 13²

Field	Data	Notes
Atkin-Lehner	2- 13+	Signs for the Atkin-Lehner involutions
Class	2704k	Isogeny class
Conductor	2704	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	720	Modular degree for the optimal curve
Δ	456976 = 24 · 134	Discriminant
Eigenvalues	2- -3  2 -1  5 13+  3  3	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-169,-845]	[a1,a2,a3,a4,a6]
j	1168128	j-invariant
L	1.324189676701	L(r)(E,1)/r!
Ω	1.324189676701	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	676d1 10816bj1 24336bv1 67600cj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2704k1

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
-	-3	2	-1	5	+	3	3	1	-1	8	3	3	-1	-4	-6	-5	-5	-7	11	14	4	-12	-9	-1

---

Quadratic twists for elliptic curve 2704k1

-4	8	-3	5	13
676d1	10816bj1	24336bv1	67600cj1	2704l1

---

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