Cremona's table of elliptic curves

13065 = 3 · 5 · 13 · 67

Field	Data	Notes
Atkin-Lehner	3- 5- 13- 67-	Signs for the Atkin-Lehner involutions
Class	13065n	Isogeny class
Conductor	13065	Conductor
∏ cp	162	Product of Tamagawa factors cp
Δ	-670737596485363875 = -1 · 33 · 53 · 133 · 676	Discriminant
Eigenvalues	0 3- 5- -1 -3 13- -3  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-507845,-144933244]	[a1,a2,a3,a4,a6]
Generators	[838:4321:1]	Generators of the group modulo torsion
j	-14484987012880034430976/670737596485363875	j-invariant
L	4.6507229954362	L(r)(E,1)/r!
Ω	0.089179279689177	Real period
R	2.897236899053	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	39195h2 65325a2	Quadratic twists by: -3 5

Hecke Eigenvalues for elliptic curve 13065n2

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

---

Quadratic twists for elliptic curve 13065n2

-3	5
39195h2	65325a2

---

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