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	345a	Isogeny class
Conductor	345	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	80	Modular degree for the optimal curve
Δ	-646875 = -1 · 32 · 55 · 23	Discriminant
Eigenvalues	0 3+ 5+  1  4  0  5  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-731,-7369]	[a1,a2,a3,a4,a6]
j	-43258336804864/646875	j-invariant
L	0.91805843012196	L(r)(E,1)/r!
Ω	0.45902921506098	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5520x1 22080bo1 1035c1 1725m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 345a1

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
0	+	+	1	4	0	5	0	-	5	3	-5	3	-4	6	-3	9	10	-7	7	-12	8	-1	16	-6

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Quadratic twists for elliptic curve 345a1

-4	8	-3	5	-7	-11	13	17	-19	-23
5520x1	22080bo1	1035c1	1725m1	16905bc1	41745h1	58305g1	99705r1	124545ba1	7935d1

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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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