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	3451a	Isogeny class
Conductor	3451	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	10032	Modular degree for the optimal curve
Δ	-16571975433083 = -1 · 711 · 172 · 29	Discriminant
Eigenvalues	0  3  0 7+  0 -6 17+ -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,1100,-195356]	[a1,a2,a3,a4,a6]
Generators	[15702:111871:216]	Generators of the group modulo torsion
j	147197952000000/16571975433083	j-invariant
L	4.5522859220499	L(r)(E,1)/r!
Ω	0.32937315000106	Real period
R	6.9105297776021	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	55216t1 31059l1 86275j1 24157f1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3451a1

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	0	+	0	-6	+	-1	-1	+	-8	6	-3	10	-9	-11	4	-10	-13	9	7	-12	0	9	-5

---

Quadratic twists for elliptic curve 3451a1

-4	-3	5	-7	17	29
55216t1	31059l1	86275j1	24157f1	58667h1	100079e1

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations