Properties

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

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Show commands: SageMath
E = EllipticCurve("hd1")
 
E.isogeny_class()
 

Elliptic curves in class 366912.hd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
366912.hd1 366912hd2 \([0, 0, 0, -173460, 12205312]\) \(1643032000/767637\) \(269669367095611392\) \([2]\) \(3686400\) \(2.0391\)  
366912.hd2 366912hd1 \([0, 0, 0, -144795, 21194656]\) \(61162984000/41067\) \(225418066630848\) \([2]\) \(1843200\) \(1.6925\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 366912.2.a.hd

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