Properties

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

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 25200m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25200.fw1 25200m1 \([0, 0, 0, -150, -625]\) \(55296/7\) \(47250000\) \([2]\) \(8192\) \(0.20180\) \(\Gamma_0(N)\)-optimal
25200.fw2 25200m2 \([0, 0, 0, 225, -3250]\) \(11664/49\) \(-5292000000\) \([2]\) \(16384\) \(0.54837\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 25200.2.a.m

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