Cremona's table of elliptic curves

988 = 2² · 13 · 19

Field	Data	Notes
Atkin-Lehner	2- 13- 19-	Signs for the Atkin-Lehner involutions
Class	988d	Isogeny class
Conductor	988	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	108	Modular degree for the optimal curve
Δ	-1426672 = -1 · 24 · 13 · 193	Discriminant
Eigenvalues	2- -2  0  2  0 13- -3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-18,-71]	[a1,a2,a3,a4,a6]
j	-42592000/89167	j-invariant
L	1.0820810042308	L(r)(E,1)/r!
Ω	1.0820810042308	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	3952i1 15808a1 8892n1 24700d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 988d1

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

---

Quadratic twists for elliptic curve 988d1

-4	8	-3	5	-7	-11	13	-19
3952i1	15808a1	8892n1	24700d1	48412f1	119548e1	12844c1	18772c1

---

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