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	1290b	Isogeny class
Conductor	1290	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	10560	Modular degree for the optimal curve
Δ	1190206406250000 = 24 · 311 · 510 · 43	Discriminant
Eigenvalues	2+ 3+ 5-  0  6  2  0 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-154527,-23386059]	[a1,a2,a3,a4,a6]
j	408076159454905367161/1190206406250000	j-invariant
L	1.2041878500974	L(r)(E,1)/r!
Ω	0.24083757001948	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	10320bg1 41280bd1 3870q1 6450bh1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1290b1

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

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Quadratic twists for elliptic curve 1290b1

-4	8	-3	5	-7	-43
10320bg1	41280bd1	3870q1	6450bh1	63210w1	55470bg1

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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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