Cremona's table of elliptic curves

41400 = 2³ · 3² · 5² · 23

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 23+	Signs for the Atkin-Lehner involutions
Class	41400r	Isogeny class
Conductor	41400	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	30720	Modular degree for the optimal curve
Δ	14486688000 = 28 · 39 · 53 · 23	Discriminant
Eigenvalues	2+ 3- 5-  0  0  0 -4  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-9255,342650]	[a1,a2,a3,a4,a6]
Generators	[50:70:1]	Generators of the group modulo torsion
j	3758161808/621	j-invariant
L	5.7231743254388	L(r)(E,1)/r!
Ω	1.2097412934774	Real period
R	2.3654538190493	Regulator
r	1	Rank of the group of rational points
S	1.0000000000006	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	82800ca1 13800s1 41400cd1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 41400r1

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
+	-	-	0	0	0	-4	2	+	6	0	-2	-6	4	-8	8	-6	10	-4	-2	16	-14	4	10	10

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Quadratic twists for elliptic curve 41400r1

-4	-3	5
82800ca1	13800s1	41400cd1

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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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