Properties

Label 196504.be
Number of curves $2$
Conductor $196504$
CM no
Rank $0$
Graph

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

Elliptic curves in class 196504.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
196504.be1 196504o2 \([0, -1, 0, -4327968, -3464003860]\) \(2471097448795250/98942809\) \(358980037949130752\) \([2]\) \(4423680\) \(2.4514\)  
196504.be2 196504o1 \([0, -1, 0, -257528, -59487844]\) \(-1041220466500/242597383\) \(-440090687923059712\) \([2]\) \(2211840\) \(2.1049\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 196504.be have rank \(0\).

Complex multiplication

The elliptic curves in class 196504.be do not have complex multiplication.

Modular form 196504.2.a.be

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} - q^{7} + q^{9} - 4 q^{13} - 2 q^{17} - 6 q^{19} + O(q^{20})\) 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.