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	348a	Isogeny class
Conductor	348	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	12	Modular degree for the optimal curve
Δ	-1392 = -1 · 24 · 3 · 29	Discriminant
Eigenvalues	2- 3+  0 -3 -3 -3  1 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,2,1]	[a1,a2,a3,a4,a6]
Generators	[0:1:1]	Generators of the group modulo torsion
j	32000/87	j-invariant
L	1.4721036783364	L(r)(E,1)/r!
Ω	3.3700624663336	Real period
R	0.14560597348392	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	1392o1 5568i1 1044e1 8700o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 348a1

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
-	+	0	-3	-3	-3	1	-4	-2	-	-2	-6	10	0	-3	4	10	-6	3	6	14	4	-18	7	0

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Quadratic twists for elliptic curve 348a1

-4	8	-3	5	-7	-11	13	17	-19	29
1392o1	5568i1	1044e1	8700o1	17052o1	42108a1	58812g1	100572i1	125628i1	10092g1

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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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