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	-2562890625 = -1 · 38 · 58	Discriminant
Eigenvalues	1 3- 5+  0  4 -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,315,1066]	[a1,a2,a3,a4,a6]
j	4733169839/3515625	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	720h6 2880r6 15a4 225c6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 45a6

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 45a6

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53
720h6	2880r6	15a4	225c6	2205j6	5445g6	7605q6	13005n6	16245d6	23805t5	37845d5	43245b5	61605k5	75645g5	83205u5	99405m5	126405s5

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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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