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Properties

Label 11271.f
Number of curves $2$
Conductor $11271$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 11271.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11271.f1 11271e1 \([1, 0, 0, -187261, -31203112]\) \(147815204204011553/15178486401\) \(74571903688113\) \([2]\) \(79872\) \(1.6948\) \(\Gamma_0(N)\)-optimal
11271.f2 11271e2 \([1, 0, 0, -172896, -36187767]\) \(-116340772335201233/47730591665289\) \(-234500396851564857\) \([2]\) \(159744\) \(2.0413\)  

Rank

sage: E.rank()
 

The elliptic curves in class 11271.f have rank \(0\).

Complex multiplication

The elliptic curves in class 11271.f do not have complex multiplication.

Modular form 11271.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} + 4 q^{5} - q^{6} + 3 q^{8} + q^{9} - 4 q^{10} - q^{12} - q^{13} + 4 q^{15} - q^{16} - q^{18} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.