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	8	Product of Tamagawa factors cp
Δ	164025 = 38 · 52	Discriminant
Eigenvalues	1 3- 5+  0  4 -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-45,-104]	[a1,a2,a3,a4,a6]
j	13997521/225	j-invariant
L	0.92159087663963	L(r)(E,1)/r!
Ω	1.8431817532793	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	720h2 2880r2 15a3 225c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 45a2

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 45a2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53
720h2	2880r2	15a3	225c2	2205j2	5445g2	7605q2	13005n2	16245d2	23805t2	37845d2	43245b2	61605k2	75645g2	83205u2	99405m2	126405s2

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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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