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Properties

Label 286650.rv
Number of curves $2$
Conductor $286650$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("rv1")
 
E.isogeny_class()
 

Elliptic curves in class 286650.rv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
286650.rv1 286650rv2 \([1, -1, 1, -38841305, 92886640697]\) \(38686490446661/141927552\) \(23774561714972250000000\) \([2]\) \(41287680\) \(3.1540\)  
286650.rv2 286650rv1 \([1, -1, 1, -3561305, -40879303]\) \(29819839301/17252352\) \(2889975213216000000000\) \([2]\) \(20643840\) \(2.8074\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 286650.rv have rank \(0\).

Complex multiplication

The elliptic curves in class 286650.rv do not have complex multiplication.

Modular form 286650.2.a.rv

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{8} + 6 q^{11} + q^{13} + q^{16} + 4 q^{17} - 2 q^{19} + O(q^{20})\) 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.