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	6422d	Isogeny class
Conductor	6422	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	567840	Modular degree for the optimal curve
Δ	-1.3153678445674E+23	Discriminant
Eigenvalues	2+  1  3 -1 -2 13-  1 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-2888552,-17551703882]	[a1,a2,a3,a4,a6]
Generators	[332151926041190:-40435769158287927:22188041000]	Generators of the group modulo torsion
j	-251347109804029/12403865550848	j-invariant
L	3.9674463845337	L(r)(E,1)/r!
Ω	0.045585773155765	Real period
R	21.758139162065	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	51376ba1 57798bw1 6422j1 122018bj1	Quadratic twists by: -4 -3 13 -19

Hecke Eigenvalues for elliptic curve 6422d1

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	3	-1	-2	-	1	-	-4	2	4	-3	-10	-11	3	0	6	6	2	3	4	-6	14	-8	-16

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Quadratic twists for elliptic curve 6422d1

-4	-3	13	-19
51376ba1	57798bw1	6422j1	122018bj1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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