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	345c	Isogeny class
Conductor	345	Conductor
∏ cp	20	Product of Tamagawa factors cp
Δ	10024505152875 = 320 · 53 · 23	Discriminant
Eigenvalues	1 3- 5+  4  4  6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-16564,-807613]	[a1,a2,a3,a4,a6]
j	502552788401502649/10024505152875	j-invariant
L	2.1067250612821	L(r)(E,1)/r!
Ω	0.42134501225643	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	5520q4 22080r3 1035g4 1725g3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 345c3

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	6	-2	-4	+	-10	-8	2	2	-8	0	-6	0	6	8	-4	10	16	-12	-10	-10

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Quadratic twists for elliptic curve 345c3

-4	8	-3	5	-7	-11	13	17	-19	-23
5520q4	22080r3	1035g4	1725g3	16905l4	41745z3	58305l3	99705j3	124545k3	7935j4

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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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