Cremona's table of elliptic curves

5040 = 2⁴ · 3² · 5 · 7

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 7-	Signs for the Atkin-Lehner involutions
Class	5040bo	Isogeny class
Conductor	5040	Conductor
∏ cp	256	Product of Tamagawa factors cp
Δ	-26885053440000 = -1 · 213 · 37 · 54 · 74	Discriminant
Eigenvalues	2- 3- 5- 7- -4 -2  6  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,933,249226]	[a1,a2,a3,a4,a6]
Generators	[-43:360:1]	Generators of the group modulo torsion
j	30080231/9003750	j-invariant
L	4.0622252856564	L(r)(E,1)/r!
Ω	0.51739273621216	Real period
R	0.49070862921705	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	630j4 20160ee4 1680r4 25200ea3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040bo4

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	-2	6	0	-8	-10	8	2	2	-8	4	-10	4	-6	0	-12	-6	8	-4	-14	2

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Quadratic twists for elliptic curve 5040bo4

-4	8	-3	5	-7
630j4	20160ee4	1680r4	25200ea3	35280em3

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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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