Cremona's table of elliptic curves

10647 = 3² · 7 · 13²

Field	Data	Notes
Atkin-Lehner	3- 7- 13+	Signs for the Atkin-Lehner involutions
Class	10647f	Isogeny class
Conductor	10647	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	-221680856943 = -1 · 38 · 7 · 136	Discriminant
Eigenvalues	-1 3- -2 7-  4 13+  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,1489,4502]	[a1,a2,a3,a4,a6]
Generators	[222:3241:1]	Generators of the group modulo torsion
j	103823/63	j-invariant
L	2.6860763145684	L(r)(E,1)/r!
Ω	0.61200653106436	Real period
R	4.3889667482747	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	3549c1 74529bc1 63a1	Quadratic twists by: -3 -7 13

Hecke Eigenvalues for elliptic curve 10647f1

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	-	4	+	6	-4	0	2	0	-6	2	-4	0	-6	12	-2	-4	0	6	-16	-12	-14	-18

---

Quadratic twists for elliptic curve 10647f1

-3	-7	13
3549c1	74529bc1	63a1

---

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