Cremona's table of elliptic curves

451 = 11 · 41

Field	Data	Notes
Atkin-Lehner	11+ 41+	Signs for the Atkin-Lehner involutions
Class	451a	Isogeny class
Conductor	451	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	36	Modular degree for the optimal curve
Δ	-18491 = -1 · 11 · 412	Discriminant
Eigenvalues	0  1 -3  4 11+ -6  2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,3,7]	[a1,a2,a3,a4,a6]
Generators	[7:20:1]	Generators of the group modulo torsion
j	2097152/18491	j-invariant
L	1.7563718021034	L(r)(E,1)/r!
Ω	2.8355647890502	Real period
R	0.30970405065083	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	7216g1 28864g1 4059e1 11275a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 451a1

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	-3	4	+	-6	2	-8	-5	-8	3	7	+	6	0	-2	9	12	-9	-13	6	10	-12	13	-5

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Quadratic twists for elliptic curve 451a1

-4	8	-3	5	-7	-11	13	41
7216g1	28864g1	4059e1	11275a1	22099b1	4961c1	76219e1	18491b1

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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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