Cremona's table of elliptic curves

6422 = 2 · 13² · 19

Field	Data	Notes
Atkin-Lehner	2- 13+ 19+	Signs for the Atkin-Lehner involutions
Class	6422h	Isogeny class
Conductor	6422	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	25536	Modular degree for the optimal curve
Δ	-45304429274 = -1 · 2 · 137 · 192	Discriminant
Eigenvalues	2-  3  3 -3  0 13+  5 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-10341,-402281]	[a1,a2,a3,a4,a6]
j	-25334470953/9386	j-invariant
L	7.5748237506823	L(r)(E,1)/r!
Ω	0.23671324220882	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	51376z1 57798r1 494c1 122018p1	Quadratic twists by: -4 -3 13 -19

Hecke Eigenvalues for elliptic curve 6422h1

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
-	3	3	-3	0	+	5	+	6	-8	-8	5	10	7	1	-10	-6	-6	4	5	-8	12	8	0	2

---

Quadratic twists for elliptic curve 6422h1

-4	-3	13	-19
51376z1	57798r1	494c1	122018p1

---

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