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	4512d	Isogeny class
Conductor	4512	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	3328	Modular degree for the optimal curve
Δ	306926309376 = 212 · 313 · 47	Discriminant
Eigenvalues	2+ 3+ -1 -1  3  2  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2781,-48843]	[a1,a2,a3,a4,a6]
j	580928771584/74933181	j-invariant
L	1.3259935248982	L(r)(E,1)/r!
Ω	0.66299676244908	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	4512m1 9024u1 13536y1 112800ca1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4512d1

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	3	2	0	0	1	-1	8	-7	-2	8	-	12	-14	2	4	0	-4	3	-4	0	-7

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Quadratic twists for elliptic curve 4512d1

-4	8	-3	5
4512m1	9024u1	13536y1	112800ca1

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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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