Cremona's table of elliptic curves

11368 = 2³ · 7² · 29

Field	Data	Notes
Atkin-Lehner	2- 7+ 29-	Signs for the Atkin-Lehner involutions
Class	11368i	Isogeny class
Conductor	11368	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	217728	Modular degree for the optimal curve
Δ	54864609211585936 = 24 · 78 · 296	Discriminant
Eigenvalues	2- -3 -1 7+  5  2 -3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-473683,124974451]	[a1,a2,a3,a4,a6]
Generators	[365:841:1]	Generators of the group modulo torsion
j	127433263474944/594823321	j-invariant
L	2.7176781022874	L(r)(E,1)/r!
Ω	0.35551855786311	Real period
R	0.63702209120069	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	22736d1 90944f1 102312g1 11368o1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 11368i1

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
-	-3	-1	+	5	2	-3	-1	9	-	-7	1	2	-4	7	3	3	-15	-13	-8	1	-17	-4	-3	18

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Quadratic twists for elliptic curve 11368i1

-4	8	-3	-7
22736d1	90944f1	102312g1	11368o1

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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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