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Properties

Label 193200.fa
Number of curves $2$
Conductor $193200$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("fa1")
 
E.isogeny_class()
 

Elliptic curves in class 193200.fa

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
193200.fa1 193200cl2 \([0, 1, 0, -144208, -20802412]\) \(5182207647625/91449288\) \(5852754432000000\) \([2]\) \(1327104\) \(1.8217\)  
193200.fa2 193200cl1 \([0, 1, 0, -208, -930412]\) \(-15625/5842368\) \(-373911552000000\) \([2]\) \(663552\) \(1.4751\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 193200.fa have rank \(0\).

Complex multiplication

The elliptic curves in class 193200.fa do not have complex multiplication.

Modular form 193200.2.a.fa

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