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	4512b	Isogeny class
Conductor	4512	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	-2192832 = -1 · 26 · 36 · 47	Discriminant
Eigenvalues	2+ 3+  2 -4  2  4 -6  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2,72]	[a1,a2,a3,a4,a6]
Generators	[-2:8:1]	Generators of the group modulo torsion
j	-21952/34263	j-invariant
L	3.3178491217086	L(r)(E,1)/r!
Ω	2.094751953454	Real period
R	1.5838863958273	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	4512r1 9024p1 13536bd1 112800cf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4512b1

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
+	+	2	-4	2	4	-6	8	-8	-2	-6	2	4	-8	+	6	0	2	-8	0	14	-16	16	-2	6

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Quadratic twists for elliptic curve 4512b1

-4	8	-3	5
4512r1	9024p1	13536bd1	112800cf1

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

Part of Computational Number Theory
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