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Properties

Label 11774.f
Number of curves $2$
Conductor $11774$
CM no
Rank $1$
Graph

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

Elliptic curves in class 11774.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11774.f1 11774l2 \([1, 0, 0, -33004642, -72964106940]\) \(6684374974140996553/2097096248576\) \(1247401755034617840896\) \([2]\) \(1075200\) \(3.0237\)  
11774.f2 11774l1 \([1, 0, 0, -1786722, -1456339388]\) \(-1060490285861833/926330847232\) \(-551003190895281897472\) \([2]\) \(537600\) \(2.6771\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 11774.f have rank \(1\).

Complex multiplication

The elliptic curves in class 11774.f do not have complex multiplication.

Modular form 11774.2.a.f

sage: E.q_eigenform(10)
 
\(q + q^{2} - 2 q^{3} + q^{4} + 2 q^{5} - 2 q^{6} + q^{7} + q^{8} + q^{9} + 2 q^{10} - 4 q^{11} - 2 q^{12} - 2 q^{13} + q^{14} - 4 q^{15} + q^{16} + 4 q^{17} + q^{18} - 2 q^{19} + O(q^{20})\) 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.