↑

Properties

Label 1411200.lw
Number of curves $2$
Conductor $1411200$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("lw1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 1411200.lw have rank \(0\).

Complex multiplication

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

Modular form 1411200.2.a.lw

Copy content sage:E.q_eigenform(10)
 
\(q - 2 q^{13} + 4 q^{17} - 2 q^{19} + O(q^{20})\) 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.lw

Copy content sage:E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
1411200.lw1 \([0, 0, 0, -7335300, -7644098000]\) \(3976047968/1575\) \(17290449993600000000\) \([2]\) \(37748736\) \(2.6556\)
1411200.lw2 \([0, 0, 0, -389550, -156579500]\) \(-19056256/19845\) \(-6808114684980000000\) \([2]\) \(18874368\) \(2.3090\)