Properties

Label 34272n
Number of curves $4$
Conductor $34272$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 34272n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
34272.h3 34272n1 \([0, 0, 0, -741, 6820]\) \(964430272/127449\) \(5946260544\) \([2, 2]\) \(14336\) \(0.60345\) \(\Gamma_0(N)\)-optimal
34272.h4 34272n2 \([0, 0, 0, 1149, 35926]\) \(449455096/1753941\) \(-654654970368\) \([4]\) \(28672\) \(0.95002\)  
34272.h2 34272n3 \([0, 0, 0, -3036, -57440]\) \(1036433728/122451\) \(365636726784\) \([2]\) \(28672\) \(0.95002\)  
34272.h1 34272n4 \([0, 0, 0, -11451, 471634]\) \(444893916104/9639\) \(3597737472\) \([2]\) \(28672\) \(0.95002\)  

Rank

sage: E.rank()
 

The elliptic curves in class 34272n have rank \(1\).

Complex multiplication

The elliptic curves in class 34272n do not have complex multiplication.

Modular form 34272.2.a.n

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} - q^{7} - 2 q^{13} + q^{17} - 8 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.