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Properties

Label 1411200.qw
Number of curves $2$
Conductor $1411200$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("qw1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 1411200.qw have rank \(1\).

Complex multiplication

The elliptic curves in class 1411200.qw do not have complex multiplication.

Modular form 1411200.2.a.qw

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

Isogeny matrix

Copy content 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

Copy content sage:E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.

Elliptic curves in class 1411200.qw

Copy content sage:E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
1411200.qw1 \([0, 0, 0, -208321050, 1157304809500]\) \(8496758995072/2025\) \(238284013974300000000\) \([2]\) \(198180864\) \(3.2884\)
1411200.qw2 \([0, 0, 0, -207549300, 1166304958000]\) \(-262583645216/4100625\) \(-15440804105534640000000000\) \([2]\) \(396361728\) \(3.6350\)