Properties

Label 141120bi
Number of curves $2$
Conductor $141120$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bi1")
 
E.isogeny_class()
 

Elliptic curves in class 141120bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141120.mn1 141120bi1 \([0, 0, 0, -90552, -7932904]\) \(2725888/675\) \(20333569192473600\) \([2]\) \(688128\) \(1.8396\) \(\Gamma_0(N)\)-optimal
141120.mn2 141120bi2 \([0, 0, 0, 218148, -50286544]\) \(2382032/3645\) \(-1756820378229719040\) \([2]\) \(1376256\) \(2.1862\)  

Rank

sage: E.rank()
 

The elliptic curves in class 141120bi have rank \(1\).

Complex multiplication

The elliptic curves in class 141120bi do not have complex multiplication.

Modular form 141120.2.a.bi

sage: E.q_eigenform(10)
 
\(q + q^{5} + 2 q^{13} + 2 q^{17} + 6 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.