Properties

Label 235200.fb
Number of curves $2$
Conductor $235200$
CM no
Rank $1$
Graph

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

Elliptic curves in class 235200.fb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235200.fb1 235200fb2 \([0, -1, 0, -1030633, -332391863]\) \(16079333824/2953125\) \(22235661000000000000\) \([2]\) \(5308416\) \(2.4308\)  
235200.fb2 235200fb1 \([0, -1, 0, 126992, -30251738]\) \(1925134784/4465125\) \(-525317491125000000\) \([2]\) \(2654208\) \(2.0843\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 235200.fb have rank \(1\).

Complex multiplication

The elliptic curves in class 235200.fb do not have complex multiplication.

Modular form 235200.2.a.fb

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