Properties

Label 458640.e
Number of curves $2$
Conductor $458640$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 458640.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
458640.e1 458640e1 \([0, 0, 0, -35868, -250733]\) \(3718856704/2132325\) \(2926099903381200\) \([2]\) \(2211840\) \(1.6574\) \(\Gamma_0(N)\)-optimal
458640.e2 458640e2 \([0, 0, 0, 142737, -2001062]\) \(14647977776/8555625\) \(-187848388859040000\) \([2]\) \(4423680\) \(2.0040\)  

Rank

sage: E.rank()
 

The elliptic curves in class 458640.e have rank \(1\).

Complex multiplication

The elliptic curves in class 458640.e do not have complex multiplication.

Modular form 458640.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{5} - 6 q^{11} + q^{13} - 2 q^{17} - 2 q^{19} + O(q^{20})\) Copy content 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.