Cremona's table of elliptic curves

345 = 3 · 5 · 23

Field	Data	Notes
Atkin-Lehner	3- 5+ 23+	Signs for the Atkin-Lehner involutions
Class	345d	Isogeny class
Conductor	345	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	26953125 = 3 · 58 · 23	Discriminant
Eigenvalues	-1 3- 5+  4 -4 -2  6  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-381,2820]	[a1,a2,a3,a4,a6]
j	6117442271569/26953125	j-invariant
L	1.0604859958981	L(r)(E,1)/r!
Ω	2.1209719917962	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	5520p3 22080q3 1035f3 1725d4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 345d4

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	-4	-2	6	8	+	6	8	6	-6	-8	-8	2	-4	-10	8	0	-6	-4	-12	6	-14

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Quadratic twists for elliptic curve 345d4

-4	8	-3	5	-7	-11	13	17	-19	-23
5520p3	22080q3	1035f3	1725d4	16905m3	41745u3	58305j3	99705l3	124545i3	7935k3

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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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