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Properties

Label 40950.cw
Number of curves $2$
Conductor $40950$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cw1")
 
E.isogeny_class()
 

Elliptic curves in class 40950.cw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40950.cw1 40950ea2 \([1, -1, 1, -826761605, 9150153361647]\) \(-5486773802537974663600129/2635437714\) \(-30019282711031250\) \([]\) \(9219840\) \(3.4006\)  
40950.cw2 40950ea1 \([1, -1, 1, 160645, 279975147]\) \(40251338884511/2997011332224\) \(-34137832206114000000\) \([]\) \(1317120\) \(2.4276\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 40950.cw have rank \(0\).

Complex multiplication

The elliptic curves in class 40950.cw do not have complex multiplication.

Modular form 40950.2.a.cw

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{7} + q^{8} - 5 q^{11} + q^{13} - q^{14} + q^{16} - 3 q^{17} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.