Cremona's table of elliptic curves

6240 = 2⁵ · 3 · 5 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 13+	Signs for the Atkin-Lehner involutions
Class	6240y	Isogeny class
Conductor	6240	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	276349320000 = 26 · 312 · 54 · 13	Discriminant
Eigenvalues	2- 3+ 5-  2  2 13+ -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-10590,-415188]	[a1,a2,a3,a4,a6]
Generators	[-61:10:1]	Generators of the group modulo torsion
j	2052450196928704/4317958125	j-invariant
L	3.9536956019291	L(r)(E,1)/r!
Ω	0.47068140445165	Real period
R	2.0999850241243	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	6240r1 12480ba2 18720h1 31200x1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6240y1

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
-	+	-	2	2	+	-2	2	-8	-6	-2	2	-2	0	6	-10	-14	-10	2	-6	2	-12	6	-18	-14

---

Quadratic twists for elliptic curve 6240y1

-4	8	-3	5	13
6240r1	12480ba2	18720h1	31200x1	81120d1

---

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