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	119574225 = 314 · 52	Discriminant
Eigenvalues	1 3- 5+  0  4 -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1215,16600]	[a1,a2,a3,a4,a6]
j	272223782641/164025	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	720h5 2880r5 15a2 225c5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 45a5

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 45a5

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53
720h5	2880r5	15a2	225c5	2205j5	5445g5	7605q5	13005n5	16245d5	23805t6	37845d6	43245b6	61605k6	75645g6	83205u6	99405m6	126405s6

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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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