Properties

Label 3648q
Number of curves $2$
Conductor $3648$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3648q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3648.v2 3648q1 \([0, 1, 0, 11, 155]\) \(131072/9747\) \(-9980928\) \([2]\) \(576\) \(0.022556\) \(\Gamma_0(N)\)-optimal
3648.v1 3648q2 \([0, 1, 0, -369, 2511]\) \(340062928/13851\) \(226934784\) \([2]\) \(1152\) \(0.36913\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3648q have rank \(1\).

Complex multiplication

The elliptic curves in class 3648q do not have complex multiplication.

Modular form 3648.2.a.q

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{5} + q^{9} - 2 q^{11} - 2 q^{13} - 2 q^{15} + 6 q^{17} + q^{19} + O(q^{20})\)  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.