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Properties

Label 80850be
Number of curves $2$
Conductor $80850$
CM no
Rank $1$
Graph

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

Elliptic curves in class 80850be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
80850.d2 80850be1 \([1, 1, 0, -34325, 292125]\) \(19465109/11088\) \(2547836156250000\) \([2]\) \(614400\) \(1.6460\) \(\Gamma_0(N)\)-optimal
80850.d1 80850be2 \([1, 1, 0, -401825, 97679625]\) \(31226116949/71148\) \(16348615335937500\) \([2]\) \(1228800\) \(1.9926\)  

Rank

sage: E.rank()
 

The elliptic curves in class 80850be have rank \(1\).

Complex multiplication

The elliptic curves in class 80850be do not have complex multiplication.

Modular form 80850.2.a.be

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - q^{11} - q^{12} - 4 q^{13} + q^{16} + 6 q^{17} - q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.