Cremona's table of elliptic curves

1421 = 7² · 29

Field	Data	Notes
Atkin-Lehner	7- 29-	Signs for the Atkin-Lehner involutions
Class	1421g	Isogeny class
Conductor	1421	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	156	Modular degree for the optimal curve
Δ	1421 = 72 · 29	Discriminant
Eigenvalues	2 -2 -1 7-  4  5 -8 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-16,-31]	[a1,a2,a3,a4,a6]
Generators	[-22:-3:8]	Generators of the group modulo torsion
j	9834496/29	j-invariant
L	3.6606522218495	L(r)(E,1)/r!
Ω	2.3752418201108	Real period
R	1.5411703308923	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	22736bn1 90944bc1 12789l1 35525o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1421g1

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

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Quadratic twists for elliptic curve 1421g1

-4	8	-3	5	-7	29
22736bn1	90944bc1	12789l1	35525o1	1421b1	41209j1

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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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