Cremona's table of elliptic curves

2088 = 2³ · 3² · 29

Field	Data	Notes
Atkin-Lehner	2+ 3+ 29+	Signs for the Atkin-Lehner involutions
Class	2088a	Isogeny class
Conductor	2088	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-9132912 = -1 · 24 · 39 · 29	Discriminant
Eigenvalues	2+ 3+  0 -1  3  1 -7 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-135,-621]	[a1,a2,a3,a4,a6]
Generators	[15:27:1]	Generators of the group modulo torsion
j	-864000/29	j-invariant
L	3.0336482430225	L(r)(E,1)/r!
Ω	0.69892328072638	Real period
R	1.0851148926781	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	4176a1 16704i1 2088i1 52200bk1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2088a1

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	3	1	-7	-6	0	+	-6	2	10	10	-1	-6	10	-12	-3	14	-16	-12	-16	-13	10

---

Quadratic twists for elliptic curve 2088a1

-4	8	-3	5	-7	29
4176a1	16704i1	2088i1	52200bk1	102312c1	60552m1

---

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