Properties

Label 141120.he
Number of curves $2$
Conductor $141120$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("he1")
 
E.isogeny_class()
 

Elliptic curves in class 141120.he

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141120.he1 141120eo2 \([0, 0, 0, -686028, 218699152]\) \(544737993463/20000\) \(1310966415360000\) \([2]\) \(1474560\) \(1.9884\)  
141120.he2 141120eo1 \([0, 0, 0, -40908, 3745168]\) \(-115501303/25600\) \(-1678037011660800\) \([2]\) \(737280\) \(1.6418\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 141120.he have rank \(0\).

Complex multiplication

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

Modular form 141120.2.a.he

sage: E.q_eigenform(10)
 
\(q - q^{5} + 4 q^{11} + 2 q^{13} + 8 q^{17} + 6 q^{19} + O(q^{20})\) 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 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.