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	4512f	Isogeny class
Conductor	4512	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	5197824 = 212 · 33 · 47	Discriminant
Eigenvalues	2+ 3-  1  1 -5 -6  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-45,27]	[a1,a2,a3,a4,a6]
Generators	[-3:12:1]	Generators of the group modulo torsion
j	2515456/1269	j-invariant
L	4.5262383036408	L(r)(E,1)/r!
Ω	2.1405143250495	Real period
R	0.35242606965004	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	4512a1 9024bk1 13536z1 112800bl1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4512f1

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
+	-	1	1	-5	-6	0	4	-3	9	0	-3	-6	0	-	-4	-6	2	16	0	-16	-11	-12	0	-15

---

Quadratic twists for elliptic curve 4512f1

-4	8	-3	5
4512a1	9024bk1	13536z1	112800bl1

---

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