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Properties

Label 272322be
Number of curves $2$
Conductor $272322$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 272322be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
272322.be2 272322be1 \([1, -1, 1, 7249, 21879]\) \(109503/64\) \(-24624540385344\) \([]\) \(829440\) \(1.2590\) \(\Gamma_0(N)\)-optimal
272322.be1 272322be2 \([1, -1, 1, -93611, -12014081]\) \(-35937/4\) \(-10097600591765124\) \([]\) \(2488320\) \(1.8083\)  

Rank

sage: E.rank()
 

The elliptic curves in class 272322be have rank \(0\).

Complex multiplication

The elliptic curves in class 272322be do not have complex multiplication.

Modular form 272322.2.a.be

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 3 q^{5} + 4 q^{7} + q^{8} + 3 q^{10} + q^{13} + 4 q^{14} + q^{16} - 3 q^{17} + 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.