Properties

Label 92400.cp
Number of curves $2$
Conductor $92400$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("cp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92400.cp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.cp1 92400bm2 \([0, -1, 0, -448, 2992]\) \(77860436/17787\) \(2276736000\) \([2]\) \(36864\) \(0.50799\)  
92400.cp2 92400bm1 \([0, -1, 0, -148, -608]\) \(11279504/693\) \(22176000\) \([2]\) \(18432\) \(0.16142\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 92400.cp have rank \(1\).

Complex multiplication

The elliptic curves in class 92400.cp do not have complex multiplication.

Modular form 92400.2.a.cp

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{7} + q^{9} - q^{11} + 4 q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})\)  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.