Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("es1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 25200es

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25200.ft2 25200es1 \([0, 0, 0, 88125, -818750]\) \(2595575/1512\) \(-44089920000000000\) \([]\) \(207360\) \(1.8832\) \(\Gamma_0(N)\)-optimal
25200.ft1 25200es2 \([0, 0, 0, -1261875, -577268750]\) \(-7620530425/526848\) \(-15362887680000000000\) \([]\) \(622080\) \(2.4325\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 25200.2.a.es

sage: E.q_eigenform(10)
 
\(q + q^{7} + 6q^{11} + q^{13} + 3q^{17} + 4q^{19} + O(q^{20})\)  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.