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
Δ	-3843168160000 = -1 · 28 · 54 · 134 · 292	Discriminant
Eigenvalues	2- -2 5-  0  2 13+  2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,1700,90948]	[a1,a2,a3,a4,a6]
Generators	[-4:290:1]	Generators of the group modulo torsion
j	2121167764784/15012375625	j-invariant
L	3.0895853836958	L(r)(E,1)/r!
Ω	0.57102876285822	Real period
R	0.45088000007671	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	30160y2 120640t2 67860i2 37700e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7540f2

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 7540f2

-4	8	-3	5	13
30160y2	120640t2	67860i2	37700e2	98020e2

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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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