Cremona's table of elliptic curves

2704 = 2⁴ · 13²

Field	Data	Notes
Atkin-Lehner	2+ 13+	Signs for the Atkin-Lehner involutions
Class	2704b	Isogeny class
Conductor	2704	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	1248	Modular degree for the optimal curve
Δ	13051691536 = 24 · 138	Discriminant
Eigenvalues	2+ -1  2  1 -1 13+  3 -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-732,-5045]	[a1,a2,a3,a4,a6]
Generators	[-21:25:1]	Generators of the group modulo torsion
j	3328	j-invariant
L	3.1006032452635	L(r)(E,1)/r!
Ω	0.93907942180916	Real period
R	3.3017476192697	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	1352c1 10816be1 24336j1 67600d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2704b1

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

---

Quadratic twists for elliptic curve 2704b1

-4	8	-3	5	13
1352c1	10816be1	24336j1	67600d1	2704c1

---

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