Cremona's table of elliptic curves

13664 = 2⁵ · 7 · 61

Field	Data	Notes
Atkin-Lehner	2+ 7- 61-	Signs for the Atkin-Lehner involutions
Class	13664g	Isogeny class
Conductor	13664	Conductor
∏ cp	140	Product of Tamagawa factors cp
deg	416640	Modular degree for the optimal curve
Δ	2849019377723158528 = 212 · 77 · 615	Discriminant
Eigenvalues	2+ -3  0 7- -1  6  3  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1284940,-554711936]	[a1,a2,a3,a4,a6]
Generators	[8158:729316:1]	Generators of the group modulo torsion
j	57281226796200168000/695561371514443	j-invariant
L	3.1360216641956	L(r)(E,1)/r!
Ω	0.14190500694472	Real period
R	0.1578531668934	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	13664c1 27328ba1 122976bo1 95648e1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13664g1

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	0	-	-1	6	3	1	-3	2	4	0	0	1	-9	8	0	-	-7	-15	-16	1	13	-17	-12

---

Quadratic twists for elliptic curve 13664g1

-4	8	-3	-7
13664c1	27328ba1	122976bo1	95648e1

---

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