Cremona's table of elliptic curves

704 = 2⁶ · 11

Field	Data	Notes
Atkin-Lehner	2+ 11+	Signs for the Atkin-Lehner involutions
Class	704a	Isogeny class
Conductor	704	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	-704 = -1 · 26 · 11	Discriminant
Eigenvalues	2+  1 -1 -2 11+ -4 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1,1]	[a1,a2,a3,a4,a6]
Generators	[0:1:1]	Generators of the group modulo torsion
j	-4096/11	j-invariant
L	2.2759885634581	L(r)(E,1)/r!
Ω	4.4873325290057	Real period
R	0.50720300952657	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	704k1 11a3 6336y1 17600e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 704a1

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	-2	+	-4	-2	0	-1	0	7	-3	-8	6	8	6	-5	-12	7	-3	4	-10	6	15	-7

---

Quadratic twists for elliptic curve 704a1

-4	8	-3	5	-7	-11	13
704k1	11a3	6336y1	17600e1	34496p1	7744f1	118976bb1

---

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