Cremona's table of elliptic curves

45 = 3² · 5

Field	Data	Notes
Atkin-Lehner	3- 5+	Signs for the Atkin-Lehner involutions
Class	45a	Isogeny class
Conductor	45	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	10935 = 37 · 5	Discriminant
Eigenvalues	1 3- 5+  0  4 -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-720,-7259]	[a1,a2,a3,a4,a6]
j	56667352321/15	j-invariant
L	0.92159087663963	L(r)(E,1)/r!
Ω	0.92159087663963	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	720h4 2880r3 15a7 225c3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 45a3

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

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Quadratic twists for elliptic curve 45a3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53
720h4	2880r3	15a7	225c3	2205j4	5445g4	7605q3	13005n3	16245d4	23805t4	37845d4	43245b4	61605k4	75645g4	83205u4	99405m4	126405s4

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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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