Cremona's table of elliptic curves

52416 = 2⁶ · 3² · 7 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7- 13-	Signs for the Atkin-Lehner involutions
Class	52416bf	Isogeny class
Conductor	52416	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	368640	Modular degree for the optimal curve
Δ	1168347608064 = 210 · 39 · 73 · 132	Discriminant
Eigenvalues	2+ 3+ -2 7-  2 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2086776,1160277480]	[a1,a2,a3,a4,a6]
Generators	[402:19656:1]	Generators of the group modulo torsion
j	49860882714802176/57967	j-invariant
L	4.8989782085615	L(r)(E,1)/r!
Ω	0.54938086059974	Real period
R	1.4862118917059	Regulator
r	1	Rank of the group of rational points
S	0.99999999999345	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	52416dz1 6552p1 52416be1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 52416bf1

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	-	2	-	-6	-4	-2	0	-4	-2	2	4	0	12	0	-6	12	-2	-2	0	4	2	-10

---

Quadratic twists for elliptic curve 52416bf1

-4	8	-3
52416dz1	6552p1	52416be1

---

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