Properties

Label 145200.o
Number of curves $4$
Conductor $145200$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 145200.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
145200.o1 145200eu4 \([0, -1, 0, -88712651408, -10169425563866688]\) \(680995599504466943307169/52207031250000000\) \(5919228191250000000000000000000\) \([2]\) \(619315200\) \(4.9529\)  
145200.o2 145200eu2 \([0, -1, 0, -5913803408, -136523554010688]\) \(201738262891771037089/45727545600000000\) \(5184584730283622400000000000000\) \([2, 2]\) \(309657600\) \(4.6063\)  
145200.o3 145200eu1 \([0, -1, 0, -1948875408, 31288058661312]\) \(7220044159551112609/448454983680000\) \(50845782997959966720000000000\) \([2]\) \(154828800\) \(4.2597\) \(\Gamma_0(N)\)-optimal
145200.o4 145200eu3 \([0, -1, 0, 13446196592, -843628194010688]\) \(2371297246710590562911/4084000833203280000\) \(-463043622404507898885120000000000\) \([2]\) \(619315200\) \(4.9529\)  

Rank

sage: E.rank()
 

The elliptic curves in class 145200.o have rank \(1\).

Complex multiplication

The elliptic curves in class 145200.o do not have complex multiplication.

Modular form 145200.2.a.o

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.