Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("gr1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 58800gr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.b2 58800gr1 \([0, -1, 0, -34800208, 78452158912]\) \(505318200625/4251528\) \(39214740585484800000000\) \([]\) \(7257600\) \(3.1607\) \(\Gamma_0(N)\)-optimal
58800.b1 58800gr2 \([0, -1, 0, -2813100208, 57429232078912]\) \(266916252066900625/162\) \(1494236419200000000\) \([]\) \(21772800\) \(3.7100\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 58800.2.a.gr

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