Properties

Label 2736.d
Number of curves $4$
Conductor $2736$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2736.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2736.d1 2736v3 \([0, 0, 0, -12607491, -17230231550]\) \(74220219816682217473/16416\) \(49017913344\) \([2]\) \(46080\) \(2.3439\)  
2736.d2 2736v2 \([0, 0, 0, -787971, -269220350]\) \(18120364883707393/269485056\) \(804678065455104\) \([2, 2]\) \(23040\) \(1.9973\)  
2736.d3 2736v4 \([0, 0, 0, -764931, -285703166]\) \(-16576888679672833/2216253521952\) \(-6617697556492320768\) \([2]\) \(46080\) \(2.3439\)  
2736.d4 2736v1 \([0, 0, 0, -50691, -3947006]\) \(4824238966273/537919488\) \(1606218984456192\) \([2]\) \(11520\) \(1.6507\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2736.2.a.d

sage: E.q_eigenform(10)
 
\(q - 2q^{5} - 4q^{11} + 2q^{13} + 6q^{17} + q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.