Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4800.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4800.p1 4800bk2 \([0, -1, 0, -4853, 131757]\) \(-30866268160/3\) \(-1228800\) \([]\) \(3456\) \(0.60179\)  
4800.p2 4800bk1 \([0, -1, 0, -53, 237]\) \(-40960/27\) \(-11059200\) \([]\) \(1152\) \(0.052484\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4800.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} + 6q^{11} + 5q^{13} + 6q^{17} + 5q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.