Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("ei1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92400.ei

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.ei1 92400ct2 \([0, 1, 0, -11208, 351588]\) \(77860436/17787\) \(35574000000000\) \([2]\) \(184320\) \(1.3127\)  
92400.ei2 92400ct1 \([0, 1, 0, -3708, -83412]\) \(11279504/693\) \(346500000000\) \([2]\) \(92160\) \(0.96614\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 92400.2.a.ei

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