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	8	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	5016453120 = 216 · 37 · 5 · 7	Discriminant
Eigenvalues	2- 3- 5- 7- -4 -2  6  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-507,-2774]	[a1,a2,a3,a4,a6]
Generators	[-10:36:1]	Generators of the group modulo torsion
j	4826809/1680	j-invariant
L	4.0622252856564	L(r)(E,1)/r!
Ω	1.0347854724243	Real period
R	1.9628345168682	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	630j1 20160ee1 1680r1 25200ea1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040bo1

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

---

Quadratic twists for elliptic curve 5040bo1

-4	8	-3	5	-7
630j1	20160ee1	1680r1	25200ea1	35280em1

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations