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	5040bg	Isogeny class
Conductor	5040	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-107138505600000000 = -1 · 213 · 314 · 58 · 7	Discriminant
Eigenvalues	2- 3- 5+ 7+  4 -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-141123,-25775678]	[a1,a2,a3,a4,a6]
Generators	[238917:22453750:27]	Generators of the group modulo torsion
j	-104094944089921/35880468750	j-invariant
L	3.5824816586481	L(r)(E,1)/r!
Ω	0.12105465005308	Real period
R	7.3984800606115	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	630d6 20160ev6 1680t6 25200er5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040bg6

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

---

Quadratic twists for elliptic curve 5040bg6

-4	8	-3	5	-7
630d6	20160ev6	1680t6	25200er5	35280fq5

---

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