Properties

Label 4800.cr
Number of curves $2$
Conductor $4800$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("cr1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4800.cr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4800.cr1 4800cq2 \([0, 1, 0, -53833, 4789463]\) \(2156689088/81\) \(648000000000\) \([2]\) \(15360\) \(1.3528\)  
4800.cr2 4800cq1 \([0, 1, 0, -3208, 81338]\) \(-29218112/6561\) \(-820125000000\) \([2]\) \(7680\) \(1.0062\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4800.cr have rank \(0\).

Complex multiplication

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

Modular form 4800.2.a.cr

sage: E.q_eigenform(10)
 
\(q + q^{3} + 4 q^{7} + q^{9} + 4 q^{13} + 8 q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.