Properties

Label 40950w
Number of curves $3$
Conductor $40950$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 40950w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40950.e3 40950w1 \([1, -1, 0, 3033, -612059]\) \(270840023/14329224\) \(-163218817125000\) \([]\) \(186624\) \(1.4069\) \(\Gamma_0(N)\)-optimal
40950.e2 40950w2 \([1, -1, 0, -27342, 16671316]\) \(-198461344537/10417365504\) \(-118660303944000000\) \([]\) \(559872\) \(1.9562\)  
40950.e1 40950w3 \([1, -1, 0, -5862717, 5465375941]\) \(-1956469094246217097/36641439744\) \(-417368899584000000\) \([]\) \(1679616\) \(2.5055\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 40950.2.a.w

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.