Cremona's table of elliptic curves

87024 = 2⁴ · 3 · 7² · 37

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 37+	Signs for the Atkin-Lehner involutions
Class	87024bg	Isogeny class
Conductor	87024	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	2236416	Modular degree for the optimal curve
Δ	-1.4114215693087E+19	Discriminant
Eigenvalues	2+ 3- -4 7-  0  0  0  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-542740,-237576676]	[a1,a2,a3,a4,a6]
Generators	[1859:71982:1]	Generators of the group modulo torsion
j	-1711503051568/1366263369	j-invariant
L	6.2293463101552	L(r)(E,1)/r!
Ω	0.085040315854228	Real period
R	6.1043069636146	Regulator
r	1	Rank of the group of rational points
S	1.0000000004931	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	43512x1 87024k1	Quadratic twists by: -4 -7

Hecke Eigenvalues for elliptic curve 87024bg1

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

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Quadratic twists for elliptic curve 87024bg1

-4	-7
43512x1	87024k1

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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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