Cremona's table of elliptic curves

10780 = 2² · 5 · 7² · 11

Field	Data	Notes
Atkin-Lehner	2- 5- 7+ 11+	Signs for the Atkin-Lehner involutions
Class	10780k	Isogeny class
Conductor	10780	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-13072251679182080 = -1 · 28 · 5 · 78 · 116	Discriminant
Eigenvalues	2-  1 5- 7+ 11+ -4  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-62540,-8175532]	[a1,a2,a3,a4,a6]
Generators	[68478:429913:216]	Generators of the group modulo torsion
j	-18330740176/8857805	j-invariant
L	5.4394888464676	L(r)(E,1)/r!
Ω	0.14754622793528	Real period
R	6.1443893693367	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	43120cg2 97020bf2 53900b2 10780e2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 10780k2

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	-	+	+	-4	6	2	-9	9	-4	2	3	11	-12	0	0	-7	5	-6	2	-16	9	9	-4

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Quadratic twists for elliptic curve 10780k2

-4	-3	5	-7	-11
43120cg2	97020bf2	53900b2	10780e2	118580q2

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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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