Cremona's table of elliptic curves

13200 = 2⁴ · 3 · 5² · 11

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 11+	Signs for the Atkin-Lehner involutions
Class	13200c	Isogeny class
Conductor	13200	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	24960	Modular degree for the optimal curve
Δ	-1234643731200 = -1 · 28 · 313 · 52 · 112	Discriminant
Eigenvalues	2+ 3+ 5+  1 11+  1  2  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-31713,-2163843]	[a1,a2,a3,a4,a6]
Generators	[10821316:315494113:12167]	Generators of the group modulo torsion
j	-551149496796160/192913083	j-invariant
L	4.2828610001458	L(r)(E,1)/r!
Ω	0.17887513199882	Real period
R	11.971650145796	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	6600n1 52800gw1 39600y1 13200bc1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13200c1

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	+	1	2	5	6	-2	-3	-10	-6	-3	-4	-10	-4	5	-5	0	-14	-4	6	-14	15

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Quadratic twists for elliptic curve 13200c1

-4	8	-3	5
6600n1	52800gw1	39600y1	13200bc1

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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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