Cremona's table of elliptic curves

13920 = 2⁵ · 3 · 5 · 29

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 29-	Signs for the Atkin-Lehner involutions
Class	13920r	Isogeny class
Conductor	13920	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	417600 = 26 · 32 · 52 · 29	Discriminant
Eigenvalues	2- 3+ 5+  0 -2 -6  4  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-346,2596]	[a1,a2,a3,a4,a6]
Generators	[10:6:1]	Generators of the group modulo torsion
j	71783828416/6525	j-invariant
L	3.3143800209537	L(r)(E,1)/r!
Ω	2.8557765180221	Real period
R	0.58029401111002	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13920z1 27840dv2 41760i1 69600s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13920r1

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	-2	-6	4	2	0	-	-6	8	-2	0	8	-6	0	14	-4	4	4	10	-4	6	8

---

Quadratic twists for elliptic curve 13920r1

-4	8	-3	5
13920z1	27840dv2	41760i1	69600s1

---

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