Properties

Label 67158.l
Number of curves $2$
Conductor $67158$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 67158.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
67158.l1 67158l2 \([1, -1, 0, -13587, -505333]\) \(380526485144625/66845573522\) \(48730423097538\) \([2]\) \(208896\) \(1.3462\)  
67158.l2 67158l1 \([1, -1, 0, 1623, -45991]\) \(648337611375/1606613372\) \(-1171221148188\) \([2]\) \(104448\) \(0.99960\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 67158.l have rank \(1\).

Complex multiplication

The elliptic curves in class 67158.l do not have complex multiplication.

Modular form 67158.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{7} - q^{8} + 6 q^{11} + q^{13} + q^{14} + q^{16} + 2 q^{17} + 4 q^{19} + O(q^{20})\) 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 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.