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	8	Product of Tamagawa factors cp
deg	40	Modular degree for the optimal curve
Δ	-46575 = -1 · 34 · 52 · 23	Discriminant
Eigenvalues	-1 3- 5+  4 -4 -2  6  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,9,0]	[a1,a2,a3,a4,a6]
j	80062991/46575	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	4	Number of elements in the torsion subgroup
Twists	5520p1 22080q1 1035f1 1725d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 345d1

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 345d1

-4	8	-3	5	-7	-11	13	17	-19	-23
5520p1	22080q1	1035f1	1725d1	16905m1	41745u1	58305j1	99705l1	124545i1	7935k1

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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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