Cremona's table of elliptic curves

4961 = 11² · 41

Field	Data	Notes
Atkin-Lehner	11- 41-	Signs for the Atkin-Lehner involutions
Class	4961c	Isogeny class
Conductor	4961	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	4320	Modular degree for the optimal curve
Δ	-32757934451 = -1 · 117 · 412	Discriminant
Eigenvalues	0  1 -3 -4 11-  6 -2  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,323,-8310]	[a1,a2,a3,a4,a6]
Generators	[18:60:1]	Generators of the group modulo torsion
j	2097152/18491	j-invariant
L	2.5252634603598	L(r)(E,1)/r!
Ω	0.57802493307354	Real period
R	0.54609743366349	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	79376s1 44649h1 124025i1 451a1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4961c1

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 4961c1

-4	-3	5	-11
79376s1	44649h1	124025i1	451a1

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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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