Properties

Label 215600.fb
Number of curves $2$
Conductor $215600$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("fb1")
 
E.isogeny_class()
 

Elliptic curves in class 215600.fb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
215600.fb1 215600ea2 \([0, 1, 0, -116424408, -483558536812]\) \(-23178622194826561/1610510\) \(-12126393023360000000\) \([]\) \(19008000\) \(3.1159\)  
215600.fb2 215600ea1 \([0, 1, 0, 195592, -134336812]\) \(109902239/1100000\) \(-8282489600000000000\) \([]\) \(3801600\) \(2.3112\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 215600.fb have rank \(1\).

Complex multiplication

The elliptic curves in class 215600.fb do not have complex multiplication.

Modular form 215600.2.a.fb

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{9} - q^{11} - 6 q^{13} - 7 q^{17} + 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.