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	348b	Isogeny class
Conductor	348	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	12	Modular degree for the optimal curve
Δ	-1392 = -1 · 24 · 3 · 29	Discriminant
Eigenvalues	2- 3-  2  1  1 -3 -3  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2,-3]	[a1,a2,a3,a4,a6]
j	-87808/87	j-invariant
L	1.8569948187176	L(r)(E,1)/r!
Ω	1.8569948187176	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1392l1 5568c1 1044f1 8700f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 348b1

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	1	1	-3	-3	2	8	-	-8	0	2	0	5	-2	-6	-12	3	4	-16	-2	-6	3	-6

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Quadratic twists for elliptic curve 348b1

-4	8	-3	5	-7	-11	13	17	-19	29
1392l1	5568c1	1044f1	8700f1	17052f1	42108d1	58812u1	100572b1	125628b1	10092a1

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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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