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Properties

Label 272832.g
Number of curves $2$
Conductor $272832$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 272832.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
272832.g1 272832g2 \([0, -1, 0, -23585, 1006881]\) \(188183524/52983\) \(408511903629312\) \([2]\) \(1572864\) \(1.5106\)  
272832.g2 272832g1 \([0, -1, 0, 3855, 101361]\) \(3286064/4263\) \(-8217193463808\) \([2]\) \(786432\) \(1.1640\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 272832.g have rank \(1\).

Complex multiplication

The elliptic curves in class 272832.g do not have complex multiplication.

Modular form 272832.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4 q^{5} + q^{9} + 4 q^{11} + 2 q^{13} + 4 q^{15} + 2 q^{17} + 8 q^{19} + O(q^{20})\) 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 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.