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Properties

Label 273273.h
Number of curves $2$
Conductor $273273$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 273273.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
273273.h1 273273h1 \([1, 1, 1, -7747048, 8274591632]\) \(263991523375/797511\) \(155338517447113193193\) \([2]\) \(9483264\) \(2.7433\) \(\Gamma_0(N)\)-optimal
273273.h2 273273h2 \([1, 1, 1, -4558863, 15147043218]\) \(-53796109375/477854091\) \(-93076015317629368757733\) \([2]\) \(18966528\) \(3.0899\)  

Rank

sage: E.rank()
 

The elliptic curves in class 273273.h have rank \(1\).

Complex multiplication

The elliptic curves in class 273273.h do not have complex multiplication.

Modular form 273273.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} + q^{6} + 3 q^{8} + q^{9} + q^{11} + q^{12} - q^{16} + 2 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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.