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
deg	44	Modular degree for the optimal curve
Δ	-17415 = -1 · 34 · 5 · 43	Discriminant
Eigenvalues	1 3+ 5+  0  4  6 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,2,7]	[a1,a2,a3,a4,a6]
j	357911/17415	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	10320bb1 41280bk1 1935k1 3225e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 645a1

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 645a1

-4	8	-3	5	-7	-11	13	-43
10320bb1	41280bk1	1935k1	3225e1	31605ba1	78045a1	109005g1	27735l1

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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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