Properties

Label 254800.ed
Number of curves $2$
Conductor $254800$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ed1")
 
E.isogeny_class()
 

Elliptic curves in class 254800.ed

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
254800.ed1 254800ed2 \([0, 0, 0, -287875, 57881250]\) \(5606442/169\) \(79530724000000000\) \([2]\) \(1843200\) \(2.0193\)  
254800.ed2 254800ed1 \([0, 0, 0, -42875, -2143750]\) \(37044/13\) \(3058874000000000\) \([2]\) \(921600\) \(1.6728\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 254800.ed have rank \(0\).

Complex multiplication

The elliptic curves in class 254800.ed do not have complex multiplication.

Modular form 254800.2.a.ed

sage: E.q_eigenform(10)
 
\(q - 3 q^{9} + 2 q^{11} + q^{13} + 4 q^{17} - 2 q^{19} + O(q^{20})\) 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.