Cremona's table of elliptic curves

4118 = 2 · 29 · 71

Field	Data	Notes
Atkin-Lehner	2+ 29- 71+	Signs for the Atkin-Lehner involutions
Class	4118b	Isogeny class
Conductor	4118	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	1488	Modular degree for the optimal curve
Δ	-491779796 = -1 · 22 · 293 · 712	Discriminant
Eigenvalues	2+ -1  1 -4 -5 -3  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-27,1057]	[a1,a2,a3,a4,a6]
Generators	[-8:33:1] [16:63:1]	Generators of the group modulo torsion
j	-2305199161/491779796	j-invariant
L	2.872423865535	L(r)(E,1)/r!
Ω	1.3514399785333	Real period
R	0.177121188705	Regulator
r	2	Rank of the group of rational points
S	0.99999999999988	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	32944i1 37062j1 102950f1 119422e1	Quadratic twists by: -4 -3 5 29

Hecke Eigenvalues for elliptic curve 4118b1

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	-4	-5	-3	0	-4	-4	-	-5	-6	-6	-7	3	3	-10	0	4	+	-2	-5	4	6	12

---

Quadratic twists for elliptic curve 4118b1

-4	-3	5	29
32944i1	37062j1	102950f1	119422e1

---

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