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	144	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	3060633600 = 212 · 36 · 52 · 41	Discriminant
Eigenvalues	2- 3- 5+ -4 -6 -4  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-516,3600]	[a1,a2,a3,a4,a6]
Generators	[-24:60:1]	Generators of the group modulo torsion
j	15195864748609/3060633600	j-invariant
L	3.6717323198394	L(r)(E,1)/r!
Ω	1.3477508534526	Real period
R	0.6810851409282	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	9840l1 39360p1 3690l1 6150c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1230h1

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 1230h1

-4	8	-3	5	-7	41
9840l1	39360p1	3690l1	6150c1	60270bd1	50430s1

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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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