Properties

Label 388416.fm
Number of curves $2$
Conductor $388416$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("fm1")
 
E.isogeny_class()
 

Elliptic curves in class 388416.fm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388416.fm1 388416fm2 \([0, 1, 0, -7056609, -7216415073]\) \(6141556990297/1019592\) \(6451487637988442112\) \([2]\) \(10616832\) \(2.6172\)  
388416.fm2 388416fm1 \([0, 1, 0, -398049, -135702369]\) \(-1102302937/616896\) \(-3903421091892166656\) \([2]\) \(5308416\) \(2.2707\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 388416.fm have rank \(0\).

Complex multiplication

The elliptic curves in class 388416.fm do not have complex multiplication.

Modular form 388416.2.a.fm

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{5} + q^{7} + q^{9} + 2 q^{11} - 4 q^{13} - 2 q^{15} - 2 q^{19} + O(q^{20})\) 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.