Properties

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

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Show commands: SageMath
E = EllipticCurve("hu1")
 
E.isogeny_class()
 

Elliptic curves in class 141120hu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141120.hj1 141120hu1 \([0, 0, 0, -144625068, -667996226352]\) \(551105805571803/1376829440\) \(835794671863034145669120\) \([2]\) \(30965760\) \(3.4676\) \(\Gamma_0(N)\)-optimal
141120.hj2 141120hu2 \([0, 0, 0, -90434988, -1174630122288]\) \(-134745327251163/903920796800\) \(-548718791015703706494566400\) \([2]\) \(61931520\) \(3.8142\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 141120.2.a.hu

sage: E.q_eigenform(10)
 
\(q - q^{5} + 4 q^{11} + 6 q^{13} + 4 q^{17} - 6 q^{19} + O(q^{20})\) 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.