Properties

Label 58800.l
Number of curves $2$
Conductor $58800$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 58800.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.l1 58800bg1 \([0, -1, 0, -1147883, -472980738]\) \(1950665639360512/492075\) \(42195431250000\) \([2]\) \(552960\) \(1.9894\) \(\Gamma_0(N)\)-optimal
58800.l2 58800bg2 \([0, -1, 0, -1143508, -476769488]\) \(-120527903507632/1937102445\) \(-2657704554540000000\) \([2]\) \(1105920\) \(2.3360\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 58800.2.a.l

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