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	1230f	Isogeny class
Conductor	1230	Conductor
∏ cp	256	Product of Tamagawa factors cp
Δ	13616100000000 = 28 · 34 · 58 · 412	Discriminant
Eigenvalues	2- 3+ 5-  0  4 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-6170,54695]	[a1,a2,a3,a4,a6]
j	25976677550021281/13616100000000	j-invariant
L	2.4823406387639	L(r)(E,1)/r!
Ω	0.62058515969098	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	8	Number of elements in the torsion subgroup
Twists	9840z2 39360bb2 3690d2 6150n2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1230f2

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
-	+	-	0	4	-2	2	-4	8	-2	0	6	-	12	-8	6	-4	-2	12	0	10	8	4	-6	-14

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Quadratic twists for elliptic curve 1230f2

-4	8	-3	5	-7	41
9840z2	39360bb2	3690d2	6150n2	60270bj2	50430z2

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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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