Properties

Label 25200.n
Number of curves $2$
Conductor $25200$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 25200.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25200.n1 25200cr2 \([0, 0, 0, -19575, -1032750]\) \(10536048/245\) \(19289340000000\) \([2]\) \(55296\) \(1.3351\)  
25200.n2 25200cr1 \([0, 0, 0, -2700, 30375]\) \(442368/175\) \(861131250000\) \([2]\) \(27648\) \(0.98852\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 25200.n have rank \(0\).

Complex multiplication

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

Modular form 25200.2.a.n

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