Properties

Label 25200.dw
Number of curves $2$
Conductor $25200$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("dw1")
 
E.isogeny_class()
 

Elliptic curves in class 25200.dw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25200.dw1 25200r2 \([0, 0, 0, -21195, -195750]\) \(208974222/117649\) \(592815428352000\) \([2]\) \(92160\) \(1.5247\)  
25200.dw2 25200r1 \([0, 0, 0, -15795, -762750]\) \(172974204/343\) \(864162432000\) \([2]\) \(46080\) \(1.1782\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 25200.dw have rank \(1\).

Complex multiplication

The elliptic curves in class 25200.dw do not have complex multiplication.

Modular form 25200.2.a.dw

sage: E.q_eigenform(10)
 
\(q + q^{7} - 2 q^{11} + 2 q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.