Cremona's table of elliptic curves

645 = 3 · 5 · 43

Field	Data	Notes
Atkin-Lehner	3+ 5- 43+	Signs for the Atkin-Lehner involutions
Class	645d	Isogeny class
Conductor	645	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	-783675 = -1 · 36 · 52 · 43	Discriminant
Eigenvalues	-2 3+ 5-  4  1  5 -3  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-18000,-923542]	[a1,a2,a3,a4,a6]
j	-645008376471556096/783675	j-invariant
L	0.82434576936255	L(r)(E,1)/r!
Ω	0.20608644234064	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	10320bi1 41280bg1 1935g1 3225h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 645d1

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	+	-	4	1	5	-3	0	3	-8	-1	8	-1	+	0	3	0	8	-9	4	4	8	15	-16	-15

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Quadratic twists for elliptic curve 645d1

-4	8	-3	5	-7	-11	13	-43
10320bi1	41280bg1	1935g1	3225h1	31605v1	78045k1	109005b1	27735j1

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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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