Cremona's table of elliptic curves

1230 = 2 · 3 · 5 · 41

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 41+	Signs for the Atkin-Lehner involutions
Class	1230h	Isogeny class
Conductor	1230	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	155072250000 = 24 · 32 · 56 · 413	Discriminant
Eigenvalues	2- 3- 5+ -4 -6 -4  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-12756,-555264]	[a1,a2,a3,a4,a6]
Generators	[-66:48:1]	Generators of the group modulo torsion
j	229545811016693569/155072250000	j-invariant
L	3.6717323198394	L(r)(E,1)/r!
Ω	0.4492502844842	Real period
R	2.0432554227846	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	9840l3 39360p3 3690l3 6150c3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1230h3

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

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Quadratic twists for elliptic curve 1230h3

-4	8	-3	5	-7	41
9840l3	39360p3	3690l3	6150c3	60270bd3	50430s3

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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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