Cremona's table of elliptic curves

7540 = 2² · 5 · 13 · 29

Field	Data	Notes
Atkin-Lehner	2- 5- 13+ 29+	Signs for the Atkin-Lehner involutions
Class	7540f	Isogeny class
Conductor	7540	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	5376	Modular degree for the optimal curve
Δ	30631250000 = 24 · 58 · 132 · 29	Discriminant
Eigenvalues	2- -2 5-  0  2 13+  2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1425,18448]	[a1,a2,a3,a4,a6]
Generators	[11:65:1]	Generators of the group modulo torsion
j	20014882963456/1914453125	j-invariant
L	3.0895853836958	L(r)(E,1)/r!
Ω	1.1420575257164	Real period
R	0.22544000003835	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	30160y1 120640t1 67860i1 37700e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7540f1

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

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Quadratic twists for elliptic curve 7540f1

-4	8	-3	5	13
30160y1	120640t1	67860i1	37700e1	98020e1

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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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