Cremona's table of elliptic curves

10241 = 7² · 11 · 19

Field	Data	Notes
Atkin-Lehner	7- 11- 19-	Signs for the Atkin-Lehner involutions
Class	10241g	Isogeny class
Conductor	10241	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2176	Modular degree for the optimal curve
Δ	-14982583 = -1 · 73 · 112 · 192	Discriminant
Eigenvalues	-1 -2  0 7- 11- -6 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,27,-176]	[a1,a2,a3,a4,a6]
Generators	[5:7:1] [11:33:1]	Generators of the group modulo torsion
j	6331625/43681	j-invariant
L	2.9925986606438	L(r)(E,1)/r!
Ω	1.1043784658043	Real period
R	1.3548791258193	Regulator
r	2	Rank of the group of rational points
S	0.99999999999957	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	92169t1 10241f1 112651i1	Quadratic twists by: -3 -7 -11

Hecke Eigenvalues for elliptic curve 10241g1

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
-1	-2	0	-	-	-6	-2	-	-8	6	-6	-10	6	-8	2	-6	6	-10	-12	0	-6	-8	-12	12	8

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Quadratic twists for elliptic curve 10241g1

-3	-7	-11
92169t1	10241f1	112651i1

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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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