Properties

Label 27225.f
Number of curves $2$
Conductor $27225$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 27225.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
27225.f1 27225l2 \([1, -1, 1, -50480, -4328728]\) \(19034163/121\) \(90432652921875\) \([2]\) \(76800\) \(1.5150\)  
27225.f2 27225l1 \([1, -1, 1, -5105, 27272]\) \(19683/11\) \(8221150265625\) \([2]\) \(38400\) \(1.1684\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 27225.f have rank \(0\).

Complex multiplication

The elliptic curves in class 27225.f do not have complex multiplication.

Modular form 27225.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - 2 q^{7} + 3 q^{8} - 2 q^{13} + 2 q^{14} - q^{16} + 2 q^{17} + 6 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.