Cremona's table of elliptic curves

13072 = 2⁴ · 19 · 43

Field	Data	Notes
Atkin-Lehner	2- 19- 43+	Signs for the Atkin-Lehner involutions
Class	13072f	Isogeny class
Conductor	13072	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	-4715203002368 = -1 · 227 · 19 · 432	Discriminant
Eigenvalues	2- -1 -2  1  2 -3  3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2624,-115712]	[a1,a2,a3,a4,a6]
Generators	[1248:44032:1]	Generators of the group modulo torsion
j	-488001047617/1151172608	j-invariant
L	3.2144511070034	L(r)(E,1)/r!
Ω	0.311379471589	Real period
R	1.290407445054	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	1634d1 52288r1 117648bv1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 13072f1

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	-2	1	2	-3	3	-	3	-1	0	-2	-8	+	4	5	1	-4	5	-4	-1	-8	6	8	16

---

Quadratic twists for elliptic curve 13072f1

-4	8	-3
1634d1	52288r1	117648bv1

---

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