Properties

Label 272.a
Number of curves $2$
Conductor $272$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 272.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
272.a1 272a2 \([0, 1, 0, -48, -140]\) \(6097250/289\) \(591872\) \([2]\) \(32\) \(-0.13184\)  
272.a2 272a1 \([0, 1, 0, -8, 4]\) \(62500/17\) \(17408\) \([2]\) \(16\) \(-0.47842\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 272.a have rank \(1\).

Complex multiplication

The elliptic curves in class 272.a do not have complex multiplication.

Modular form 272.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} + q^{9} - 2 q^{11} - 6 q^{13} - q^{17} - 4 q^{19} + O(q^{20})\) 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.