Properties

Label 214080.j
Number of curves $2$
Conductor $214080$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 214080.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
214080.j1 214080cu2 \([0, -1, 0, -14480001, -30801412479]\) \(-1280824409818832580001/822726139895701410\) \(-215672721216818750423040\) \([]\) \(26869248\) \(3.1786\)  
214080.j2 214080cu1 \([0, -1, 0, -435201, 123315201]\) \(-34773983355859201/4877010000000\) \(-1278478909440000000\) \([]\) \(3838464\) \(2.2057\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 214080.j have rank \(1\).

Complex multiplication

The elliptic curves in class 214080.j do not have complex multiplication.

Modular form 214080.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{7} + q^{9} - 5 q^{11} + q^{15} - 3 q^{17} + 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.