Properties

Label 14504h
Number of curves $2$
Conductor $14504$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 14504h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14504.f1 14504h1 \([0, 0, 0, -827218, 289586325]\) \(33256413948450816/2481997\) \(4672071440848\) \([2]\) \(117504\) \(1.8807\) \(\Gamma_0(N)\)-optimal
14504.f2 14504h2 \([0, 0, 0, -825503, 290846850]\) \(-2065624967846736/17960084863\) \(-540924422156054272\) \([2]\) \(235008\) \(2.2273\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14504h have rank \(1\).

Complex multiplication

The elliptic curves in class 14504h do not have complex multiplication.

Modular form 14504.2.a.h

sage: E.q_eigenform(10)
 
\(q + 4 q^{5} - 3 q^{9} - 4 q^{11} + 4 q^{13} - 2 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.