Cremona's table of elliptic curves

1428 = 2² · 3 · 7 · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 17+	Signs for the Atkin-Lehner involutions
Class	1428a	Isogeny class
Conductor	1428	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-4608076032 = -1 · 28 · 32 · 76 · 17	Discriminant
Eigenvalues	2- 3+  2 7+  0  6 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-252,-3528]	[a1,a2,a3,a4,a6]
j	-6940769488/18000297	j-invariant
L	1.6711107220571	L(r)(E,1)/r!
Ω	0.55703690735236	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5712v2 22848v2 4284e2 35700bi2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1428a2

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	+	0	6	+	-2	0	8	0	2	2	8	-8	-2	12	-4	12	0	8	-8	0	10	12

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Quadratic twists for elliptic curve 1428a2

-4	8	-3	5	-7	17
5712v2	22848v2	4284e2	35700bi2	9996o2	24276k2

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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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