Cremona's table of elliptic curves

22512 = 2⁴ · 3 · 7 · 67

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 67+	Signs for the Atkin-Lehner involutions
Class	22512o	Isogeny class
Conductor	22512	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	2769100762146582528 = 212 · 36 · 712 · 67	Discriminant
Eigenvalues	2- 3+  2 7-  4  2 -6  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4207152,3321908352]	[a1,a2,a3,a4,a6]
Generators	[1339503:13713462:1331]	Generators of the group modulo torsion
j	2010612953066556130993/676049990758443	j-invariant
L	5.8647507691222	L(r)(E,1)/r!
Ω	0.25007418102897	Real period
R	7.8173480964606	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1407c3 90048cb4 67536bw4	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 22512o4

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	-6	8	0	-2	-8	-10	6	-4	4	-2	0	-14	+	0	2	8	-16	-14	-18

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Quadratic twists for elliptic curve 22512o4

-4	8	-3
1407c3	90048cb4	67536bw4

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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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