Cremona's table of elliptic curves

14415 = 3 · 5 · 31²

Field	Data	Notes
Atkin-Lehner	3+ 5- 31-	Signs for the Atkin-Lehner involutions
Class	14415c	Isogeny class
Conductor	14415	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	30720	Modular degree for the optimal curve
Δ	412689211665 = 3 · 5 · 317	Discriminant
Eigenvalues	-1 3+ 5- -4  4 -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-9630,358410]	[a1,a2,a3,a4,a6]
Generators	[390660:1381830:4913]	Generators of the group modulo torsion
j	111284641/465	j-invariant
L	2.3199728124226	L(r)(E,1)/r!
Ω	0.95001079228534	Real period
R	9.7681956089855	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	43245c1 72075bd1 465b1	Quadratic twists by: -3 5 -31

Hecke Eigenvalues for elliptic curve 14415c1

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

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Quadratic twists for elliptic curve 14415c1

-3	5	-31
43245c1	72075bd1	465b1

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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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