Cremona's table of elliptic curves

1272 = 2³ · 3 · 53

Field	Data	Notes
Atkin-Lehner	2- 3- 53-	Signs for the Atkin-Lehner involutions
Class	1272b	Isogeny class
Conductor	1272	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	208	Modular degree for the optimal curve
Δ	-325632 = -1 · 211 · 3 · 53	Discriminant
Eigenvalues	2- 3-  4  1 -5  0  2  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-16,32]	[a1,a2,a3,a4,a6]
j	-235298/159	j-invariant
L	2.8131093088001	L(r)(E,1)/r!
Ω	2.8131093088001	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	2544b1 10176c1 3816b1 31800a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1272b1

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
-	-	4	1	-5	0	2	5	-1	9	-4	-8	3	4	-2	-	-12	-5	11	-5	-2	4	-8	8	5

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Quadratic twists for elliptic curve 1272b1

-4	8	-3	5	-7	53
2544b1	10176c1	3816b1	31800a1	62328bk1	67416d1

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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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