Properties

Label 58800fv
Number of curves $2$
Conductor $58800$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("fv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 58800fv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.s2 58800fv1 \([0, -1, 0, 460192, -147525888]\) \(596183/864\) \(-15619751368704000000\) \([]\) \(1088640\) \(2.3684\) \(\Gamma_0(N)\)-optimal
58800.s1 58800fv2 \([0, -1, 0, -13945808, -20143053888]\) \(-16591834777/98304\) \(-1777180600172544000000\) \([]\) \(3265920\) \(2.9177\)  

Rank

sage: E.rank()
 

The elliptic curves in class 58800fv have rank \(1\).

Complex multiplication

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

Modular form 58800.2.a.fv

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