Cremona's table of elliptic curves

1421 = 7² · 29

Field	Data	Notes
Atkin-Lehner	7+ 29+	Signs for the Atkin-Lehner involutions
Class	1421a	Isogeny class
Conductor	1421	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	588	Modular degree for the optimal curve
Δ	167179229 = 78 · 29	Discriminant
Eigenvalues	0 -2 -3 7+  6 -1  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-457,3560]	[a1,a2,a3,a4,a6]
Generators	[10:9:1]	Generators of the group modulo torsion
j	1835008/29	j-invariant
L	1.4075470645197	L(r)(E,1)/r!
Ω	1.8162670118135	Real period
R	2.3249011109567	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	22736q1 90944k1 12789c1 35525a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1421a1

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
0	-2	-3	+	6	-1	0	2	0	+	2	-10	-12	8	6	9	-12	2	-4	9	2	-10	-3	-6	8

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Quadratic twists for elliptic curve 1421a1

-4	8	-3	5	-7	29
22736q1	90944k1	12789c1	35525a1	1421c1	41209a1

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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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