Properties

Label 2736.w
Number of curves $2$
Conductor $2736$
CM no
Rank $0$
Graph

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

Elliptic curves in class 2736.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2736.w1 2736x2 \([0, 0, 0, -10083, -431390]\) \(-37966934881/4952198\) \(-14787183992832\) \([]\) \(7200\) \(1.2602\)  
2736.w2 2736x1 \([0, 0, 0, -3, 2050]\) \(-1/608\) \(-1815478272\) \([]\) \(1440\) \(0.45552\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2736.w have rank \(0\).

Complex multiplication

The elliptic curves in class 2736.w do not have complex multiplication.

Modular form 2736.2.a.w

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.