Cremona's table of elliptic curves

5415 = 3 · 5 · 19²

Field	Data	Notes
Atkin-Lehner	3- 5+ 19+	Signs for the Atkin-Lehner involutions
Class	5415f	Isogeny class
Conductor	5415	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	12160	Modular degree for the optimal curve
Δ	-14520946400055 = -1 · 32 · 5 · 199	Discriminant
Eigenvalues	-1 3- 5+  2 -4  2  6 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,4144,-151545]	[a1,a2,a3,a4,a6]
j	24389/45	j-invariant
L	1.4713888904337	L(r)(E,1)/r!
Ω	0.36784722260843	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	86640bs1 16245f1 27075b1 5415a1	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 5415f1

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	-	+	2	-4	2	6	+	6	0	4	-6	8	6	-2	-14	12	-10	-12	12	-10	-4	6	0	18

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Quadratic twists for elliptic curve 5415f1

-4	-3	5	-19
86640bs1	16245f1	27075b1	5415a1

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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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