Cremona's table of elliptic curves

11552 = 2⁵ · 19²

Field	Data	Notes
Atkin-Lehner	2+ 19+	Signs for the Atkin-Lehner involutions
Class	11552d	Isogeny class
Conductor	11552	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	38304	Modular degree for the optimal curve
Δ	-8695584276992 = -1 · 29 · 198	Discriminant
Eigenvalues	2+  3  2 -2 -3  2 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-6859,260642]	[a1,a2,a3,a4,a6]
Generators	[2638974:12378898:59319]	Generators of the group modulo torsion
j	-4104	j-invariant
L	8.0929587150648	L(r)(E,1)/r!
Ω	0.69887663505377	Real period
R	11.579953183643	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	11552r1 23104h1 103968bn1 11552u1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 11552d1

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
+	3	2	-2	-3	2	-6	+	-4	-6	-8	-8	-3	-8	10	2	-3	14	7	-2	11	-4	-15	-18	-3

---

Quadratic twists for elliptic curve 11552d1

-4	8	-3	-19
11552r1	23104h1	103968bn1	11552u1

---

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