Properties

Label 58800.o
Number of curves $6$
Conductor $58800$
CM no
Rank $0$
Graph

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

Elliptic curves in class 58800.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.o1 58800bf4 \([0, -1, 0, -8232408, 9094305312]\) \(32779037733124/315\) \(592950960000000\) \([4]\) \(1179648\) \(2.4130\)  
58800.o2 58800bf6 \([0, -1, 0, -7938408, -8577152688]\) \(14695548366242/57421875\) \(216180037500000000000\) \([2]\) \(2359296\) \(2.7596\)  
58800.o3 58800bf3 \([0, -1, 0, -735408, 8823312]\) \(23366901604/13505625\) \(25422772410000000000\) \([2, 2]\) \(1179648\) \(2.4130\)  
58800.o4 58800bf2 \([0, -1, 0, -514908, 142005312]\) \(32082281296/99225\) \(46694888100000000\) \([2, 2]\) \(589824\) \(2.0664\)  
58800.o5 58800bf1 \([0, -1, 0, -18783, 4082562]\) \(-24918016/229635\) \(-6754082028750000\) \([2]\) \(294912\) \(1.7199\) \(\Gamma_0(N)\)-optimal
58800.o6 58800bf5 \([0, -1, 0, 2939592, 67623312]\) \(746185003198/432360075\) \(-1627735374837600000000\) \([2]\) \(2359296\) \(2.7596\)  

Rank

sage: E.rank()
 

The elliptic curves in class 58800.o have rank \(0\).

Complex multiplication

The elliptic curves in class 58800.o do not have complex multiplication.

Modular form 58800.2.a.o

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

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.