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	40	Product of Tamagawa factors cp
Δ	488076890625 = 310 · 56 · 232	Discriminant
Eigenvalues	1 3- 5+  4  4  6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-2189,20387]	[a1,a2,a3,a4,a6]
j	1159246431432649/488076890625	j-invariant
L	2.1067250612821	L(r)(E,1)/r!
Ω	0.84269002451286	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	5520q2 22080r2 1035g2 1725g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 345c2

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 345c2

-4	8	-3	5	-7	-11	13	17	-19	-23
5520q2	22080r2	1035g2	1725g2	16905l2	41745z2	58305l2	99705j2	124545k2	7935j2

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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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