Properties

Label 283920s
Number of curves $2$
Conductor $283920$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 283920s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
283920.s1 283920s1 \([0, -1, 0, -2461541, -1485658695]\) \(-225596176962617344/15946875\) \(-116597426400000\) \([]\) \(3525120\) \(2.1521\) \(\Gamma_0(N)\)-optimal
283920.s2 283920s2 \([0, -1, 0, -2218181, -1791294519]\) \(-165082666931912704/94207763671875\) \(-688810992187500000000\) \([]\) \(10575360\) \(2.7015\)  

Rank

sage: E.rank()
 

The elliptic curves in class 283920s have rank \(0\).

Complex multiplication

The elliptic curves in class 283920s do not have complex multiplication.

Modular form 283920.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - q^{7} + q^{9} + 3 q^{11} + q^{15} - 3 q^{17} - 2 q^{19} + O(q^{20})\) 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 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.