Cremona's table of elliptic curves

40656 = 2⁴ · 3 · 7 · 11²

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 11+	Signs for the Atkin-Lehner involutions
Class	40656cc	Isogeny class
Conductor	40656	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	-447216 = -1 · 24 · 3 · 7 · 113	Discriminant
Eigenvalues	2- 3- -3 7+ 11+  1 -4  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-502,-4501]	[a1,a2,a3,a4,a6]
Generators	[1245:7271:27]	Generators of the group modulo torsion
j	-658266368/21	j-invariant
L	5.1252135205921	L(r)(E,1)/r!
Ω	0.50422076658078	Real period
R	5.0823110235478	Regulator
r	1	Rank of the group of rational points
S	1.0000000000003	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	10164j1 121968dn1 40656cy1	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 40656cc1

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
-	-	-3	+	+	1	-4	5	-4	5	-2	1	-8	-12	7	6	11	-2	-3	-8	11	2	8	-6	-12

---

Quadratic twists for elliptic curve 40656cc1

-4	-3	-11
10164j1	121968dn1	40656cy1

---

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