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	4	Product of Tamagawa factors cp
Δ	20988075 = 3 · 52 · 234	Discriminant
Eigenvalues	-1 3- 5+  4 -4 -2  6  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-411,-3234]	[a1,a2,a3,a4,a6]
j	7679186557489/20988075	j-invariant
L	1.0604859958981	L(r)(E,1)/r!
Ω	1.0604859958981	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	5520p4 22080q4 1035f4 1725d3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 345d3

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 345d3

-4	8	-3	5	-7	-11	13	17	-19	-23
5520p4	22080q4	1035f4	1725d3	16905m4	41745u4	58305j4	99705l4	124545i4	7935k4

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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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