Cremona's table of elliptic curves

1645 = 5 · 7 · 47

Field	Data	Notes
Atkin-Lehner	5+ 7+ 47-	Signs for the Atkin-Lehner involutions
Class	1645a	Isogeny class
Conductor	1645	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-541205 = -1 · 5 · 72 · 472	Discriminant
Eigenvalues	1  0 5+ 7+  6  2 -4  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,20,-15]	[a1,a2,a3,a4,a6]
j	860085351/541205	j-invariant
L	1.6809098624556	L(r)(E,1)/r!
Ω	1.6809098624556	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	26320h2 105280n2 14805k2 8225c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1645a2

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

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Quadratic twists for elliptic curve 1645a2

-4	8	-3	5	-7	-47
26320h2	105280n2	14805k2	8225c2	11515h2	77315d2

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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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