Cremona's table of elliptic curves

3451 = 7 · 17 · 29

Field	Data	Notes
Atkin-Lehner	7+ 17- 29-	Signs for the Atkin-Lehner involutions
Class	3451d	Isogeny class
Conductor	3451	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	-2874683 = -1 · 73 · 172 · 29	Discriminant
Eigenvalues	0 -1 -2 7+  4 -4 17- -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-379,2971]	[a1,a2,a3,a4,a6]
Generators	[13:8:1]	Generators of the group modulo torsion
j	-6036521254912/2874683	j-invariant
L	1.87309331026	L(r)(E,1)/r!
Ω	2.5063764045385	Real period
R	0.37366560482859	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	55216w1 31059e1 86275g1 24157d1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3451d1

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

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Quadratic twists for elliptic curve 3451d1

-4	-3	5	-7	17	29
55216w1	31059e1	86275g1	24157d1	58667e1	100079a1

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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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