Cremona's table of elliptic curves

4512 = 2⁵ · 3 · 47

Field	Data	Notes
Atkin-Lehner	2- 3- 47+	Signs for the Atkin-Lehner involutions
Class	4512o	Isogeny class
Conductor	4512	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	577536 = 212 · 3 · 47	Discriminant
Eigenvalues	2- 3-  3 -3 -3 -2 -4  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-189,939]	[a1,a2,a3,a4,a6]
Generators	[5:12:1]	Generators of the group modulo torsion
j	183250432/141	j-invariant
L	4.6699218015601	L(r)(E,1)/r!
Ω	2.8836600569404	Real period
R	0.80972127597366	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	4512e1 9024h1 13536p1 112800l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4512o1

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
-	-	3	-3	-3	-2	-4	0	-1	3	-4	1	6	-4	+	-8	-6	2	-8	0	8	1	-16	-16	-7

---

Quadratic twists for elliptic curve 4512o1

-4	8	-3	5
4512e1	9024h1	13536p1	112800l1

---

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