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Properties

Label 126350bm
Number of curves $2$
Conductor $126350$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bm1")
 
E.isogeny_class()
 

Elliptic curves in class 126350bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
126350.ba2 126350bm1 \([1, -1, 0, 2578508, -7660225584]\) \(141526649406897/1973822685184\) \(-26442284761088000000000\) \([2]\) \(11404800\) \(2.9832\) \(\Gamma_0(N)\)-optimal
126350.ba1 126350bm2 \([1, -1, 0, -46061492, -112771265584]\) \(806764685224507983/56693912375296\) \(759499111293272000000000\) \([2]\) \(22809600\) \(3.3297\)  

Rank

sage: E.rank()
 

The elliptic curves in class 126350bm have rank \(1\).

Complex multiplication

The elliptic curves in class 126350bm do not have complex multiplication.

Modular form 126350.2.a.bm

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{7} - q^{8} - 3 q^{9} - 4 q^{11} - 6 q^{13} - q^{14} + q^{16} - 4 q^{17} + 3 q^{18} + O(q^{20})\) 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 Cremona 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 Cremona labels.