Cremona's table of elliptic curves

2704 = 2⁴ · 13²

Field	Data	Notes
Atkin-Lehner	2- 13+	Signs for the Atkin-Lehner involutions
Class	2704f	Isogeny class
Conductor	2704	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1008	Modular degree for the optimal curve
Δ	1003976272 = 24 · 137	Discriminant
Eigenvalues	2-  0 -2 -2 -2 13+  6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-676,6591]	[a1,a2,a3,a4,a6]
j	442368/13	j-invariant
L	0.77722229478245	L(r)(E,1)/r!
Ω	1.5544445895649	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	676a1 10816ba1 24336br1 67600bf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2704f1

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	-2	-2	+	6	-6	-8	2	10	6	6	-4	-2	6	-10	-2	10	10	-2	4	-6	6	-2

---

Quadratic twists for elliptic curve 2704f1

-4	8	-3	5	13
676a1	10816ba1	24336br1	67600bf1	208c2

---

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