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	1230i	Isogeny class
Conductor	1230	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	6720	Modular degree for the optimal curve
Δ	729711914062500 = 22 · 36 · 514 · 41	Discriminant
Eigenvalues	2- 3- 5+ -2  2  6  0 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-52706,4467936]	[a1,a2,a3,a4,a6]
j	16192145593815022369/729711914062500	j-invariant
L	3.0090859973973	L(r)(E,1)/r!
Ω	0.50151433289955	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	9840o1 39360t1 3690i1 6150f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1230i1

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	6	0	-2	8	0	0	-2	-	4	2	-6	12	2	-4	4	2	0	-12	-2	-16

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Quadratic twists for elliptic curve 1230i1

-4	8	-3	5	-7	41
9840o1	39360t1	3690i1	6150f1	60270x1	50430q1

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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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