Cremona's table of elliptic curves

1456 = 2⁴ · 7 · 13

Field	Data	Notes
Atkin-Lehner	2+ 7- 13-	Signs for the Atkin-Lehner involutions
Class	1456d	Isogeny class
Conductor	1456	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-3937024 = -1 · 28 · 7 · 133	Discriminant
Eigenvalues	2+  0 -1 7- -2 13-  0  7	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-68,236]	[a1,a2,a3,a4,a6]
Generators	[1:13:1]	Generators of the group modulo torsion
j	-135834624/15379	j-invariant
L	2.6206124680231	L(r)(E,1)/r!
Ω	2.4096994253562	Real period
R	0.36250890054966	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	728c1 5824y1 13104z1 36400a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1456d1

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
+	0	-1	-	-2	-	0	7	3	-9	-5	-8	-10	-5	-7	3	0	6	10	-4	-11	11	-11	-3	-15

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Quadratic twists for elliptic curve 1456d1

-4	8	-3	5	-7	13
728c1	5824y1	13104z1	36400a1	10192d1	18928a1

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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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