Cremona's table of elliptic curves

47040 = 2⁶ · 3 · 5 · 7²

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 7+	Signs for the Atkin-Lehner involutions
Class	47040ev	Isogeny class
Conductor	47040	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	184320	Modular degree for the optimal curve
Δ	-663828480000 = -1 · 214 · 33 · 54 · 74	Discriminant
Eigenvalues	2- 3+ 5- 7+ -2 -1  0  3	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-318565,-69100163]	[a1,a2,a3,a4,a6]
Generators	[684:5705:1]	Generators of the group modulo torsion
j	-90888126966784/16875	j-invariant
L	5.3207681556362	L(r)(E,1)/r!
Ω	0.10047775565492	Real period
R	4.4128906285158	Regulator
r	1	Rank of the group of rational points
S	0.99999999999804	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	47040cw1 11760s1 47040ga1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 47040ev1

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	-1	0	3	0	0	9	-3	2	3	6	0	-4	-2	5	-14	1	-9	-6	-4	-14

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Quadratic twists for elliptic curve 47040ev1

-4	8	-7
47040cw1	11760s1	47040ga1

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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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