Cremona's table of elliptic curves

1422 = 2 · 3² · 79

Field	Data	Notes
Atkin-Lehner	2+ 3- 79-	Signs for the Atkin-Lehner involutions
Class	1422d	Isogeny class
Conductor	1422	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	448	Modular degree for the optimal curve
Δ	14743296 = 28 · 36 · 79	Discriminant
Eigenvalues	2+ 3-  3 -3  2 -5 -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-78,-172]	[a1,a2,a3,a4,a6]
Generators	[-4:10:1]	Generators of the group modulo torsion
j	72511713/20224	j-invariant
L	2.2478716504796	L(r)(E,1)/r!
Ω	1.6393554300742	Real period
R	0.68559618287839	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	11376m1 45504bb1 158a1 35550bz1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1422d1

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	2	-5	-6	0	2	-6	-10	-10	-2	4	3	12	1	12	-8	3	-6	-	-14	7	-11

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Quadratic twists for elliptic curve 1422d1

-4	8	-3	5	-7	-79
11376m1	45504bb1	158a1	35550bz1	69678n1	112338j1

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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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