Properties

Label 27753.c
Number of curves $4$
Conductor $27753$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 27753.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
27753.c1 27753d4 \([1, 0, 0, -123224, 16622493]\) \(347873904937/395307\) \(235137822554547\) \([2]\) \(145152\) \(1.6710\)  
27753.c2 27753d2 \([1, 0, 0, -9689, 114504]\) \(169112377/88209\) \(52468770322089\) \([2, 2]\) \(72576\) \(1.3244\)  
27753.c3 27753d1 \([1, 0, 0, -5484, -155457]\) \(30664297/297\) \(176662526337\) \([2]\) \(36288\) \(0.97787\) \(\Gamma_0(N)\)-optimal
27753.c4 27753d3 \([1, 0, 0, 36566, 900839]\) \(9090072503/5845851\) \(-3477248505891171\) \([2]\) \(145152\) \(1.6710\)  

Rank

sage: E.rank()
 

The elliptic curves in class 27753.c have rank \(0\).

Complex multiplication

The elliptic curves in class 27753.c do not have complex multiplication.

Modular form 27753.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} - 2 q^{5} - q^{6} + 4 q^{7} + 3 q^{8} + q^{9} + 2 q^{10} - q^{11} - q^{12} - 2 q^{13} - 4 q^{14} - 2 q^{15} - q^{16} + 2 q^{17} - q^{18} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.