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	1456i	Isogeny class
Conductor	1456	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	36673373772578816 = 217 · 73 · 138	Discriminant
Eigenvalues	2-  0  2 7- -4 13+ -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-946139,-354106230]	[a1,a2,a3,a4,a6]
Generators	[-70845:34146:125]	Generators of the group modulo torsion
j	22868021811807457713/8953460393696	j-invariant
L	2.9195874627631	L(r)(E,1)/r!
Ω	0.15308090581049	Real period
R	6.3573952333794	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	182a4 5824bd3 13104cd4 36400bk4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1456i3

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

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Quadratic twists for elliptic curve 1456i3

-4	8	-3	5	-7	13
182a4	5824bd3	13104cd4	36400bk4	10192bf4	18928j3

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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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