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	8	Product of Tamagawa factors cp
Δ	416025 = 32 · 52 · 432	Discriminant
Eigenvalues	1 3+ 5+  0  4  6 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-43,88]	[a1,a2,a3,a4,a6]
j	9116230969/416025	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	4	Number of elements in the torsion subgroup
Twists	10320bb2 41280bk2 1935k2 3225e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 645a2

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 645a2

-4	8	-3	5	-7	-11	13	-43
10320bb2	41280bk2	1935k2	3225e2	31605ba2	78045a2	109005g2	27735l2

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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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