Properties

Label 92400.hr
Number of curves $4$
Conductor $92400$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("hr1")
 
E.isogeny_class()
 

Elliptic curves in class 92400.hr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.hr1 92400he4 \([0, 1, 0, -5653208, 5171325588]\) \(312196988566716625/25367712678\) \(1623533611392000000\) \([2]\) \(1990656\) \(2.5394\)  
92400.hr2 92400he3 \([0, 1, 0, -329208, 92229588]\) \(-61653281712625/21875235228\) \(-1400015054592000000\) \([2]\) \(995328\) \(2.1928\)  
92400.hr3 92400he2 \([0, 1, 0, -145208, -10730412]\) \(5290763640625/2291573592\) \(146660709888000000\) \([2]\) \(663552\) \(1.9901\)  
92400.hr4 92400he1 \([0, 1, 0, 30792, -1226412]\) \(50447927375/39517632\) \(-2529128448000000\) \([2]\) \(331776\) \(1.6435\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 92400.2.a.hr

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.