Cremona's table of elliptic curves

1290 = 2 · 3 · 5 · 43

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 43+	Signs for the Atkin-Lehner involutions
Class	1290k	Isogeny class
Conductor	1290	Conductor
∏ cp	28	Product of Tamagawa factors cp
Δ	898614000000 = 27 · 35 · 56 · 432	Discriminant
Eigenvalues	2- 3+ 5+ -4 -4  4  4  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-165776,-26048527]	[a1,a2,a3,a4,a6]
j	503835593418244309249/898614000000	j-invariant
L	1.656216906	L(r)(E,1)/r!
Ω	0.23660241514285	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	10320bd2 41280bv2 3870i2 6450n2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1290k2

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

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Quadratic twists for elliptic curve 1290k2

-4	8	-3	5	-7	-43
10320bd2	41280bv2	3870i2	6450n2	63210ct2	55470o2

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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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