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Properties

Label 124579b
Number of curves $3$
Conductor $124579$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 124579b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
124579.b2 124579b1 \([0, 1, 1, -10039, 384524]\) \(-43614208/91\) \(-233481103219\) \([]\) \(207360\) \(1.0669\) \(\Gamma_0(N)\)-optimal
124579.b3 124579b2 \([0, 1, 1, 17341, 1930125]\) \(224755712/753571\) \(-1933457015756539\) \([]\) \(622080\) \(1.6163\)  
124579.b1 124579b3 \([0, 1, 1, -160629, -61124646]\) \(-178643795968/524596891\) \(-1345972097317994419\) \([]\) \(1866240\) \(2.1656\)  

Rank

sage: E.rank()
 

The elliptic curves in class 124579b have rank \(0\).

Complex multiplication

The elliptic curves in class 124579b do not have complex multiplication.

Modular form 124579.2.a.b

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - 2 q^{4} + 3 q^{5} + q^{7} + q^{9} + 4 q^{12} - q^{13} - 6 q^{15} + 4 q^{16} + 6 q^{17} + 7 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.