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	10780c	Isogeny class
Conductor	10780	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-7971896240 = -1 · 24 · 5 · 77 · 112	Discriminant
Eigenvalues	2-  0 5+ 7- 11+ -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,392,-3087]	[a1,a2,a3,a4,a6]
Generators	[18:99:1]	Generators of the group modulo torsion
j	3538944/4235	j-invariant
L	3.8143380596276	L(r)(E,1)/r!
Ω	0.70518661501929	Real period
R	1.802992275798	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	43120bm1 97020ct1 53900f1 1540a1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 10780c1

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	6	-4	-2	-2	10	2	12	0	0	-6	-6	0	2	-8	10	0	-4	6	2

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Quadratic twists for elliptic curve 10780c1

-4	-3	5	-7	-11
43120bm1	97020ct1	53900f1	1540a1	118580e1

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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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