Properties

Label 14784bs
Number of curves $2$
Conductor $14784$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bs1")
 
E.isogeny_class()
 

Elliptic curves in class 14784bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14784.bh2 14784bs1 \([0, -1, 0, -25921, -2500127]\) \(-7347774183121/6119866368\) \(-1604286249172992\) \([2]\) \(129024\) \(1.6155\) \(\Gamma_0(N)\)-optimal
14784.bh1 14784bs2 \([0, -1, 0, -476481, -126404127]\) \(45637459887836881/13417633152\) \(3517352024997888\) \([2]\) \(258048\) \(1.9621\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14784bs have rank \(0\).

Complex multiplication

The elliptic curves in class 14784bs do not have complex multiplication.

Modular form 14784.2.a.bs

sage: E.q_eigenform(10)
 
\(q - q^{3} + 4 q^{5} - q^{7} + q^{9} - q^{11} + 6 q^{13} - 4 q^{15} - 4 q^{17} - 2 q^{19} + O(q^{20})\) 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 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.