Cremona's table of elliptic curves

2704 = 2⁴ · 13²

Field	Data	Notes
Atkin-Lehner	2+ 13+	Signs for the Atkin-Lehner involutions
Class	2704a	Isogeny class
Conductor	2704	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2688	Modular degree for the optimal curve
Δ	-128508962816 = -1 · 211 · 137	Discriminant
Eigenvalues	2+ -1  1  5 -2 13+ -3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2760,59344]	[a1,a2,a3,a4,a6]
Generators	[-30:338:1]	Generators of the group modulo torsion
j	-235298/13	j-invariant
L	3.197754448436	L(r)(E,1)/r!
Ω	1.028566057806	Real period
R	0.38861802119655	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	1352a1 10816bc1 24336e1 67600e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2704a1

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	1	5	-2	+	-3	-2	-4	-6	-4	-11	-8	1	9	-12	6	0	6	7	2	-12	-16	10	10

---

Quadratic twists for elliptic curve 2704a1

-4	8	-3	5	13
1352a1	10816bc1	24336e1	67600e1	208b1

---

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