Cremona's table of elliptic curves

47040 = 2⁶ · 3 · 5 · 7²

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 7-	Signs for the Atkin-Lehner involutions
Class	47040eq	Isogeny class
Conductor	47040	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	1708019812167782400 = 212 · 310 · 52 · 710	Discriminant
Eigenvalues	2- 3+ 5+ 7- -4 -6 -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3889881,2953553625]	[a1,a2,a3,a4,a6]
Generators	[153:48600:1]	Generators of the group modulo torsion
j	13507798771700416/3544416225	j-invariant
L	2.8041186105484	L(r)(E,1)/r!
Ω	0.25926688573096	Real period
R	2.7038919785521	Regulator
r	1	Rank of the group of rational points
S	1.0000000000071	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	47040gh2 23520w1 6720ci2	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 47040eq2

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

---

Quadratic twists for elliptic curve 47040eq2

-4	8	-7
47040gh2	23520w1	6720ci2

---

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