Cremona's table of elliptic curves

348 = 2² · 3 · 29

Field	Data	Notes
Atkin-Lehner	2- 3- 29+	Signs for the Atkin-Lehner involutions
Class	348d	Isogeny class
Conductor	348	Conductor
∏ cp	21	Product of Tamagawa factors cp
deg	84	Modular degree for the optimal curve
Δ	-1014768 = -1 · 24 · 37 · 29	Discriminant
Eigenvalues	2- 3- -4 -3 -1 -3 -5  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-50,129]	[a1,a2,a3,a4,a6]
Generators	[10:-27:1]	Generators of the group modulo torsion
j	-881395456/63423	j-invariant
L	1.6385158325408	L(r)(E,1)/r!
Ω	2.724644682803	Real period
R	0.028636601295863	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	1392j1 5568h1 1044k1 8700d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 348d1

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
-	-	-4	-3	-1	-3	-5	4	-6	+	2	6	6	-12	7	-12	-10	10	-13	-2	14	-8	6	5	0

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Quadratic twists for elliptic curve 348d1

-4	8	-3	5	-7	-11	13	17	-19	29
1392j1	5568h1	1044k1	8700d1	17052d1	42108f1	58812p1	100572h1	125628f1	10092c1

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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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