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	10780h	Isogeny class
Conductor	10780	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	82944	Modular degree for the optimal curve
Δ	20425393248722000 = 24 · 53 · 78 · 116	Discriminant
Eigenvalues	2-  2 5+ 7- 11-  4  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-121781,14882750]	[a1,a2,a3,a4,a6]
j	106110329552896/10850811125	j-invariant
L	3.3556025922832	L(r)(E,1)/r!
Ω	0.37284473247591	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	43120bk1 97020co1 53900v1 1540c1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 10780h1

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
-	2	+	-	-	4	0	4	6	-6	4	2	6	-4	-6	-6	0	10	2	12	-8	-16	12	18	10

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Quadratic twists for elliptic curve 10780h1

-4	-3	5	-7	-11
43120bk1	97020co1	53900v1	1540c1	118580l1

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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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