Cremona's table of elliptic curves

1113 = 3 · 7 · 53

Field	Data	Notes
Atkin-Lehner	3+ 7+ 53+	Signs for the Atkin-Lehner involutions
Class	1113a	Isogeny class
Conductor	1113	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-3339 = -1 · 32 · 7 · 53	Discriminant
Eigenvalues	0 3+ -1 7+  5  2 -2  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-1,3]	[a1,a2,a3,a4,a6]
Generators	[1:1:1]	Generators of the group modulo torsion
j	-262144/3339	j-invariant
L	1.829292370558	L(r)(E,1)/r!
Ω	3.7895756802744	Real period
R	0.24135846924497	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	17808x1 71232be1 3339a1 27825o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1113a1

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

---

Quadratic twists for elliptic curve 1113a1

-4	8	-3	5	-7	53
17808x1	71232be1	3339a1	27825o1	7791e1	58989i1

---

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