Properties

Label 117600.f
Number of curves $2$
Conductor $117600$
CM no
Rank $1$
Graph

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

Elliptic curves in class 117600.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
117600.f1 117600cc2 \([0, -1, 0, -59208, 5339412]\) \(195112/9\) \(1058841000000000\) \([2]\) \(691200\) \(1.6445\)  
117600.f2 117600cc1 \([0, -1, 0, 2042, 316912]\) \(64/3\) \(-44118375000000\) \([2]\) \(345600\) \(1.2979\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 117600.f have rank \(1\).

Complex multiplication

The elliptic curves in class 117600.f do not have complex multiplication.

Modular form 117600.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} - 6 q^{11} + 2 q^{13} + 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.