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Properties

Label 134310.a
Number of curves $2$
Conductor $134310$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 134310.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
134310.a1 134310cm1 \([1, 1, 0, -131408, -18198528]\) \(106429035419/1278720\) \(3015154871435520\) \([2]\) \(1317888\) \(1.7814\) \(\Gamma_0(N)\)-optimal
134310.a2 134310cm2 \([1, 1, 0, -24928, -46713872]\) \(-726572699/399200400\) \(-941293661426276400\) \([2]\) \(2635776\) \(2.1279\)  

Rank

sage: E.rank()
 

The elliptic curves in class 134310.a have rank \(0\).

Complex multiplication

The elliptic curves in class 134310.a do not have complex multiplication.

Modular form 134310.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - 4 q^{7} - q^{8} + q^{9} + q^{10} - q^{12} + 4 q^{14} + q^{15} + q^{16} + 6 q^{17} - q^{18} + O(q^{20})\) 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.