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	645a	Isogeny class
Conductor	645	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	80625 = 3 · 54 · 43	Discriminant
Eigenvalues	1 3+ 5+  0  4  6 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-688,6667]	[a1,a2,a3,a4,a6]
j	36097320816649/80625	j-invariant
L	1.4773816654528	L(r)(E,1)/r!
Ω	2.9547633309056	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	10320bb3 41280bk4 1935k3 3225e4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 645a4

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

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Quadratic twists for elliptic curve 645a4

-4	8	-3	5	-7	-11	13	-43
10320bb3	41280bk4	1935k3	3225e4	31605ba4	78045a4	109005g4	27735l4

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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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