Cremona's table of elliptic curves

6405 = 3 · 5 · 7 · 61

Field	Data	Notes
Atkin-Lehner	3- 5+ 7+ 61-	Signs for the Atkin-Lehner involutions
Class	6405j	Isogeny class
Conductor	6405	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	5673132675 = 312 · 52 · 7 · 61	Discriminant
Eigenvalues	1 3- 5+ 7+  4 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-56949,5226097]	[a1,a2,a3,a4,a6]
Generators	[11:2139:1]	Generators of the group modulo torsion
j	20425422893207394889/5673132675	j-invariant
L	5.3420520789847	L(r)(E,1)/r!
Ω	1.0823226020089	Real period
R	3.2904866312929	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	102480bg4 19215r3 32025j4 44835k4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6405j3

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	-	+	+	4	-2	2	-4	8	-6	-8	-2	6	-12	8	2	0	-	-12	0	-6	-8	-12	2	2

---

Quadratic twists for elliptic curve 6405j3

-4	-3	5	-7
102480bg4	19215r3	32025j4	44835k4

---

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