Properties

Label 87120.fe
Number of curves $2$
Conductor $87120$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("fe1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 87120.fe

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.fe1 87120fo2 \([0, 0, 0, -475167, -126117574]\) \(-296587984/125\) \(-5000563975968000\) \([]\) \(570240\) \(1.9735\)  
87120.fe2 87120fo1 \([0, 0, 0, 3993, -673486]\) \(176/5\) \(-200022559038720\) \([]\) \(190080\) \(1.4242\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 87120.fe have rank \(1\).

Complex multiplication

The elliptic curves in class 87120.fe do not have complex multiplication.

Modular form 87120.2.a.fe

sage: E.q_eigenform(10)
 
\(q + q^{5} + q^{7} + 2q^{13} - 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.