Cremona's table of elliptic curves

44352 = 2⁶ · 3² · 7 · 11

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 11-	Signs for the Atkin-Lehner involutions
Class	44352bp	Isogeny class
Conductor	44352	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	81920	Modular degree for the optimal curve
Δ	26627292990144 = 26 · 38 · 78 · 11	Discriminant
Eigenvalues	2+ 3- -2 7+ 11- -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-8391,-160900]	[a1,a2,a3,a4,a6]
Generators	[8508:144100:27]	Generators of the group modulo torsion
j	1400416996672/570715299	j-invariant
L	4.1826731839747	L(r)(E,1)/r!
Ω	0.51691391330353	Real period
R	8.0916243040463	Regulator
r	1	Rank of the group of rational points
S	0.99999999999717	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	44352cd1 22176k3 14784c1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 44352bp1

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	+	-	-2	-2	4	-4	-6	-4	2	6	-12	4	6	4	-2	12	12	2	-8	12	6	18

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Quadratic twists for elliptic curve 44352bp1

-4	8	-3
44352cd1	22176k3	14784c1

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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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