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	7540b	Isogeny class
Conductor	7540	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	482560 = 28 · 5 · 13 · 29	Discriminant
Eigenvalues	2-  1 5+  3  0 13+ -3  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-21,-25]	[a1,a2,a3,a4,a6]
j	4194304/1885	j-invariant
L	2.3168511786478	L(r)(E,1)/r!
Ω	2.3168511786478	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	30160p1 120640bp1 67860t1 37700d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7540b1

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
-	1	+	3	0	+	-3	1	6	+	-5	0	3	4	-4	10	14	0	11	8	2	14	1	-2	-14

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Quadratic twists for elliptic curve 7540b1

-4	8	-3	5	13
30160p1	120640bp1	67860t1	37700d1	98020h1

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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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