Cremona's table of elliptic curves

7744 = 2⁶ · 11²

Field	Data	Notes
Atkin-Lehner	2+ 11+	Signs for the Atkin-Lehner involutions
Class	7744c	Isogeny class
Conductor	7744	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-21807104 = -1 · 214 · 113	Discriminant
Eigenvalues	2+ -1 -1 -4 11+  4 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,59,-163]	[a1,a2,a3,a4,a6]
Generators	[4:11:1]	Generators of the group modulo torsion
j	1024	j-invariant
L	2.4907546925253	L(r)(E,1)/r!
Ω	1.1707189620612	Real period
R	1.063771397424	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	7744q1 968a1 69696ba1 7744b1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 7744c1

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

---

Quadratic twists for elliptic curve 7744c1

-4	8	-3	-11
7744q1	968a1	69696ba1	7744b1

---

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