Properties

Label 366912.ls
Number of curves $2$
Conductor $366912$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ls1")
 
E.isogeny_class()
 

Elliptic curves in class 366912.ls

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
366912.ls1 366912ls2 \([0, 0, 0, -25284, 1240288]\) \(5088448/1053\) \(369916827291648\) \([2]\) \(1474560\) \(1.5105\)  
366912.ls2 366912ls1 \([0, 0, 0, 3381, 116620]\) \(778688/1521\) \(-8348817282624\) \([2]\) \(737280\) \(1.1640\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 366912.ls have rank \(1\).

Complex multiplication

The elliptic curves in class 366912.ls do not have complex multiplication.

Modular form 366912.2.a.ls

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