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	8800r	Isogeny class
Conductor	8800	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	6240	Modular degree for the optimal curve
Δ	-55000000000 = -1 · 29 · 510 · 11	Discriminant
Eigenvalues	2- -2 5+  0 11+ -1 -4  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-208,-11412]	[a1,a2,a3,a4,a6]
j	-200/11	j-invariant
L	0.49101751761296	L(r)(E,1)/r!
Ω	0.49101751761296	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8800y1 17600ck1 79200bh1 8800j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8800r1

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	+	0	+	-1	-4	1	-7	-9	1	-8	8	11	-8	2	4	-2	-10	7	-16	4	-1	-5	-3

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Quadratic twists for elliptic curve 8800r1

-4	8	-3	5	-11
8800y1	17600ck1	79200bh1	8800j1	96800v1

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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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