Cremona's table of elliptic curves

3458 = 2 · 7 · 13 · 19

Field	Data	Notes
Atkin-Lehner	2- 7- 13- 19-	Signs for the Atkin-Lehner involutions
Class	3458f	Isogeny class
Conductor	3458	Conductor
∏ cp	162	Product of Tamagawa factors cp
Δ	-330799583296 = -1 · 26 · 73 · 133 · 193	Discriminant
Eigenvalues	2- -2 -3 7- -3 13-  6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,288,-27584]	[a1,a2,a3,a4,a6]
Generators	[30:76:1]	Generators of the group modulo torsion
j	2641234272767/330799583296	j-invariant
L	3.1007495795137	L(r)(E,1)/r!
Ω	0.45587400689779	Real period
R	0.37787604233193	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	27664l2 110656p2 31122o2 86450h2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3458f2

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	-3	-	-3	-	6	-	0	0	5	-7	0	-10	6	0	3	-10	-4	-6	2	-1	-6	-6	-10

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Quadratic twists for elliptic curve 3458f2

-4	8	-3	5	-7	13	-19
27664l2	110656p2	31122o2	86450h2	24206k2	44954c2	65702k2

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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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