Cremona's table of elliptic curves

8800 = 2⁵ · 5² · 11

Field	Data	Notes
Atkin-Lehner	2+ 5+ 11+	Signs for the Atkin-Lehner involutions
Class	8800a	Isogeny class
Conductor	8800	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	3025000000 = 26 · 58 · 112	Discriminant
Eigenvalues	2+  0 5+  0 11+  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-925,-10500]	[a1,a2,a3,a4,a6]
Generators	[1090:12375:8]	Generators of the group modulo torsion
j	87528384/3025	j-invariant
L	4.1744942062893	L(r)(E,1)/r!
Ω	0.86753110591871	Real period
R	4.8119245267506	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	8800u1 17600k2 79200du1 1760j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8800a1

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

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Quadratic twists for elliptic curve 8800a1

-4	8	-3	5	-11
8800u1	17600k2	79200du1	1760j1	96800bl1

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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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