Cremona's table of elliptic curves

71104 = 2⁶ · 11 · 101

Field	Data	Notes
Atkin-Lehner	2+ 11- 101-	Signs for the Atkin-Lehner involutions
Class	71104i	Isogeny class
Conductor	71104	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	273408	Modular degree for the optimal curve
Δ	-25629294592 = -1 · 221 · 112 · 101	Discriminant
Eigenvalues	2+  2  0 -1 11-  4  3 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-374593,88369473]	[a1,a2,a3,a4,a6]
Generators	[291:1980:1]	Generators of the group modulo torsion
j	-22175014984908625/97768	j-invariant
L	9.3659873436571	L(r)(E,1)/r!
Ω	0.80307853823975	Real period
R	2.9156511151773	Regulator
r	1	Rank of the group of rational points
S	1.0000000001369	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	71104m1 2222a1	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 71104i1

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
+	2	0	-1	-	4	3	-5	0	-3	-4	-2	12	1	6	-9	-6	13	-14	6	2	14	6	-6	17

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Quadratic twists for elliptic curve 71104i1

-4	8
71104m1	2222a1

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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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