Properties

Label 92400.hi
Number of curves $2$
Conductor $92400$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("hi1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92400.hi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.hi1 92400gz2 \([0, 1, 0, -10716133, 255264377363]\) \(-2126464142970105856/438611057788643355\) \(-28071107698473174720000000\) \([]\) \(28800000\) \(3.5624\)  
92400.hi2 92400gz1 \([0, 1, 0, -3576133, -3049482637]\) \(-79028701534867456/16987307596875\) \(-1087187686200000000000\) \([]\) \(5760000\) \(2.7576\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 92400.hi have rank \(0\).

Complex multiplication

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

Modular form 92400.2.a.hi

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.