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	345f	Isogeny class
Conductor	345	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-18862875 = -1 · 38 · 53 · 23	Discriminant
Eigenvalues	-2 3- 5- -5 -2 -6  1  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-100,406]	[a1,a2,a3,a4,a6]
Generators	[5:7:1]	Generators of the group modulo torsion
j	-111701610496/18862875	j-invariant
L	1.0776581097355	L(r)(E,1)/r!
Ω	2.0934610738452	Real period
R	0.021448892362972	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5520w1 22080g1 1035a1 1725h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 345f1

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
-2	-	-	-5	-2	-6	1	2	+	-1	-5	-7	-7	-8	-12	9	3	12	-1	5	-2	-8	3	8	14

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Quadratic twists for elliptic curve 345f1

-4	8	-3	5	-7	-11	13	17	-19	-23
5520w1	22080g1	1035a1	1725h1	16905f1	41745bd1	58305h1	99705e1	124545r1	7935h1

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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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