Properties

Label 17787.f
Number of curves $2$
Conductor $17787$
CM no
Rank $1$
Graph

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

Elliptic curves in class 17787.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17787.f1 17787m2 \([0, 1, 1, -5409224, 4844375036]\) \(-1713910976512/1594323\) \(-16282337120241102603\) \([]\) \(764400\) \(2.6093\)  
17787.f2 17787m1 \([0, 1, 1, -13834, -685184]\) \(-28672/3\) \(-30638089873083\) \([]\) \(58800\) \(1.3268\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 17787.f have rank \(1\).

Complex multiplication

The elliptic curves in class 17787.f do not have complex multiplication.

Modular form 17787.2.a.f

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

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.