Properties

Label 388080.bf
Number of curves $2$
Conductor $388080$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bf1")
 
E.isogeny_class()
 

Elliptic curves in class 388080.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388080.bf1 388080bf2 \([0, 0, 0, -3454195563, -71617414709862]\) \(1400976587098424349/129687123005000\) \(421920334239200365346426880000\) \([2]\) \(433520640\) \(4.4233\)  
388080.bf2 388080bf1 \([0, 0, 0, 250204437, -5291614469862]\) \(532445465175651/4026275000000\) \(-13098966608068263014400000000\) \([2]\) \(216760320\) \(4.0767\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 388080.bf have rank \(1\).

Complex multiplication

The elliptic curves in class 388080.bf do not have complex multiplication.

Modular form 388080.2.a.bf

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{11} - 2 q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.