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	645b	Isogeny class
Conductor	645	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	72	Modular degree for the optimal curve
Δ	29025 = 33 · 52 · 43	Discriminant
Eigenvalues	1 3+ 5-  4 -2  2  0  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-22,31]	[a1,a2,a3,a4,a6]
j	1263214441/29025	j-invariant
L	1.8623340368723	L(r)(E,1)/r!
Ω	3.7246680737446	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	10320bj1 41280bh1 1935f1 3225g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 645b1

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	+	-	4	-2	2	0	6	0	10	8	-4	-10	+	0	12	-6	-10	12	4	-8	-16	-12	-10	6

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Quadratic twists for elliptic curve 645b1

-4	8	-3	5	-7	-11	13	-43
10320bj1	41280bh1	1935f1	3225g1	31605r1	78045j1	109005a1	27735i1

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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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