Properties

Label 271950.be
Number of curves $2$
Conductor $271950$
CM no
Rank $0$
Graph

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

Elliptic curves in class 271950.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
271950.be1 271950be2 \([1, 1, 0, -6930616375, -222081073152875]\) \(58389789169255064704903/621457920000\) \(391844822979960000000000\) \([2]\) \(272498688\) \(4.0989\)  
271950.be2 271950be1 \([1, 1, 0, -432824375, -3475856896875]\) \(-14221861969864791943/46510217625600\) \(-29325860055436492800000000\) \([2]\) \(136249344\) \(3.7524\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 271950.be have rank \(0\).

Complex multiplication

The elliptic curves in class 271950.be do not have complex multiplication.

Modular form 271950.2.a.be

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - q^{12} - 6 q^{13} + q^{16} + 2 q^{17} - q^{18} + 6 q^{19} + O(q^{20})\) 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.