Properties

Label 126350.i
Number of curves $2$
Conductor $126350$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 126350.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
126350.i1 126350bx1 \([1, 0, 1, -14709987576, -686700474702202]\) \(3830972064521089212269/1001428288\) \(92017726693909625000000\) \([2]\) \(151200000\) \(4.2186\) \(\Gamma_0(N)\)-optimal
126350.i2 126350bx2 \([1, 0, 1, -14708182576, -686877422462202]\) \(-3829561990703458000109/1958708234387912\) \(-179978817399870733965765625000\) \([2]\) \(302400000\) \(4.5652\)  

Rank

sage: E.rank()
 

The elliptic curves in class 126350.i have rank \(0\).

Complex multiplication

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

Modular form 126350.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} - 2 q^{3} + q^{4} + 2 q^{6} + q^{7} - q^{8} + q^{9} + 4 q^{11} - 2 q^{12} + 2 q^{13} - q^{14} + q^{16} + 6 q^{17} - q^{18} + O(q^{20})\) 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.