Cremona's table of elliptic curves

6405 = 3 · 5 · 7 · 61

Field	Data	Notes
Atkin-Lehner	3+ 5+ 7- 61-	Signs for the Atkin-Lehner involutions
Class	6405d	Isogeny class
Conductor	6405	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	4487921672535 = 33 · 5 · 74 · 614	Discriminant
Eigenvalues	1 3+ 5+ 7- -4  2  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-4518,55377]	[a1,a2,a3,a4,a6]
Generators	[64:151:1]	Generators of the group modulo torsion
j	10202640382603369/4487921672535	j-invariant
L	3.7438087403057	L(r)(E,1)/r!
Ω	0.69732433468915	Real period
R	1.3422049662065	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	102480bw3 19215y4 32025u3 44835y3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6405d3

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	+	+	-	-4	2	6	0	0	-6	0	-6	6	4	-8	10	4	-	-12	8	14	4	-4	10	-10

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Quadratic twists for elliptic curve 6405d3

-4	-3	5	-7
102480bw3	19215y4	32025u3	44835y3

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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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