Properties

Label 14994ce
Number of curves $4$
Conductor $14994$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ce1")
 
E.isogeny_class()
 

Elliptic curves in class 14994ce

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14994.ce2 14994ce1 \([1, -1, 1, -112685, 14582229]\) \(1845026709625/793152\) \(68025570403392\) \([2]\) \(69120\) \(1.6144\) \(\Gamma_0(N)\)-optimal
14994.ce3 14994ce2 \([1, -1, 1, -95045, 19288581]\) \(-1107111813625/1228691592\) \(-105380111751154632\) \([2]\) \(138240\) \(1.9610\)  
14994.ce1 14994ce3 \([1, -1, 1, -330980, -55327737]\) \(46753267515625/11591221248\) \(994134084093739008\) \([2]\) \(207360\) \(2.1637\)  
14994.ce4 14994ce4 \([1, -1, 1, 797980, -351566841]\) \(655215969476375/1001033261568\) \(-85854739836665737728\) \([2]\) \(414720\) \(2.5103\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14994ce have rank \(0\).

Complex multiplication

The elliptic curves in class 14994ce do not have complex multiplication.

Modular form 14994.2.a.ce

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{8} - 2 q^{13} + q^{16} - q^{17} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.