Properties

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

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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 126350ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
126350.u2 126350ba1 \([1, -1, 0, -8412992, -7493899584]\) \(104487111/21952\) \(13835235042274625000000\) \([2]\) \(8208000\) \(2.9632\) \(\Gamma_0(N)\)-optimal
126350.u1 126350ba2 \([1, -1, 0, -42707992, 100844005416]\) \(13669062471/941192\) \(593185702437524546875000\) \([2]\) \(16416000\) \(3.3098\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 126350.2.a.ba

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