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	988c	Isogeny class
Conductor	988	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	120	Modular degree for the optimal curve
Δ	-822016 = -1 · 28 · 132 · 19	Discriminant
Eigenvalues	2-  0 -3  3  3 13+ -7 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,16,36]	[a1,a2,a3,a4,a6]
Generators	[8:26:1]	Generators of the group modulo torsion
j	1769472/3211	j-invariant
L	2.250212502288	L(r)(E,1)/r!
Ω	1.9393544816601	Real period
R	0.19338157133963	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	3952e1 15808i1 8892k1 24700l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 988c1

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	-3	3	3	+	-7	-	0	-8	2	-8	2	1	-7	-4	-12	-9	2	4	-13	6	4	-6	4

---

Quadratic twists for elliptic curve 988c1

-4	8	-3	5	-7	-11	13	-19
3952e1	15808i1	8892k1	24700l1	48412l1	119548i1	12844b1	18772g1

---

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