Cremona's table of elliptic curves

158 = 2 · 79

Field	Data	Notes
Atkin-Lehner	2+ 79+	Signs for the Atkin-Lehner involutions
Class	158b	Isogeny class
Conductor	158	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	316 = 22 · 79	Discriminant
Eigenvalues	2+ -1 -1 -3  4 -7 -4 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-3,1]	[a1,a2,a3,a4,a6]
Generators	[0:1:1]	Generators of the group modulo torsion
j	4826809/316	j-invariant
L	0.84513994322837	L(r)(E,1)/r!
Ω	5.337584627434	Real period
R	0.079168762859941	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	1264g1 5056a1 1422f1 3950g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 158b1

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
+	-1	-1	-3	4	-7	-4	-6	6	4	8	10	-8	-8	-3	2	1	0	-4	-11	-6	+	6	-15	1

---

Quadratic twists for elliptic curve 158b1

-4	8	-3	5	-7	-11	13	17	-19	-23	-79
1264g1	5056a1	1422f1	3950g1	7742c1	19118i1	26702g1	45662f1	57038p1	83582i1	12482c1

---

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