Properties

Label 4800.z
Number of curves $2$
Conductor $4800$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 4800.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4800.z1 4800bt2 \([0, -1, 0, -193, 1057]\) \(195112/9\) \(36864000\) \([2]\) \(1536\) \(0.21339\)  
4800.z2 4800bt1 \([0, -1, 0, 7, 57]\) \(64/3\) \(-1536000\) \([2]\) \(768\) \(-0.13318\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4800.z have rank \(1\).

Complex multiplication

The elliptic curves in class 4800.z do not have complex multiplication.

Modular form 4800.2.a.z

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2 q^{7} + q^{9} - 6 q^{11} - 2 q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.