Cremona's table of elliptic curves

1827 = 3² · 7 · 29

Field	Data	Notes
Atkin-Lehner	3- 7- 29+	Signs for the Atkin-Lehner involutions
Class	1827a	Isogeny class
Conductor	1827	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	-1035909 = -1 · 36 · 72 · 29	Discriminant
Eigenvalues	1 3- -1 7-  5 -5  4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,0,49]	[a1,a2,a3,a4,a6]
Generators	[0:7:1]	Generators of the group modulo torsion
j	-1/1421	j-invariant
L	3.4668099568825	L(r)(E,1)/r!
Ω	2.2023973598107	Real period
R	0.78705369433889	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	29232z1 116928ch1 203b1 45675l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1827a1

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	-	-1	-	5	-5	4	-4	-6	+	7	-10	0	-9	-7	-3	0	14	-6	-8	-16	-9	-16	6	0

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Quadratic twists for elliptic curve 1827a1

-4	8	-3	5	-7	29
29232z1	116928ch1	203b1	45675l1	12789e1	52983g1

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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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