Cremona's table of elliptic curves

12272 = 2⁴ · 13 · 59

Field	Data	Notes
Atkin-Lehner	2+ 13- 59-	Signs for the Atkin-Lehner involutions
Class	12272d	Isogeny class
Conductor	12272	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	7488	Modular degree for the optimal curve
Δ	-92678144 = -1 · 211 · 13 · 592	Discriminant
Eigenvalues	2+  1  3 -3  2 13- -7 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3424,75988]	[a1,a2,a3,a4,a6]
Generators	[6:236:1]	Generators of the group modulo torsion
j	-2168312432834/45253	j-invariant
L	5.9823725451799	L(r)(E,1)/r!
Ω	1.7566257911441	Real period
R	0.42570055154459	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	6136f1 49088o1 110448t1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 12272d1

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	3	-3	2	-	-7	-2	2	4	8	-7	0	5	-1	0	-	-10	0	3	4	8	2	-14	-14

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Quadratic twists for elliptic curve 12272d1

-4	8	-3
6136f1	49088o1	110448t1

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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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