Cremona's table of elliptic curves

11200 = 2⁶ · 5² · 7

Field	Data	Notes
Atkin-Lehner	2- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	11200cn	Isogeny class
Conductor	11200	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	-35000000 = -1 · 26 · 57 · 7	Discriminant
Eigenvalues	2- -1 5+ 7- -3  5 -3  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-133,-613]	[a1,a2,a3,a4,a6]
Generators	[62:475:1]	Generators of the group modulo torsion
j	-262144/35	j-invariant
L	3.6494744767281	L(r)(E,1)/r!
Ω	0.69729622539986	Real period
R	2.6168752560186	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	11200c1 2800s1 100800nn1 2240w1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 11200cn1

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	+	-	-3	5	-3	2	-6	-3	4	2	-12	10	9	12	0	-8	4	0	-2	1	-12	-12	1

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Quadratic twists for elliptic curve 11200cn1

-4	8	-3	5	-7
11200c1	2800s1	100800nn1	2240w1	78400hn1

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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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