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Properties

Label 65025.ch
Number of curves $2$
Conductor $65025$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ch1")
 
E.isogeny_class()
 

Elliptic curves in class 65025.ch

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
65025.ch1 65025bt2 \([0, 0, 1, -541875, 157369531]\) \(-102400/3\) \(-515516244169921875\) \([]\) \(1228800\) \(2.1775\)  
65025.ch2 65025bt1 \([0, 0, 1, 4335, -485159]\) \(20480/243\) \(-106897448391075\) \([]\) \(245760\) \(1.3728\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 65025.ch have rank \(0\).

Complex multiplication

The elliptic curves in class 65025.ch do not have complex multiplication.

Modular form 65025.2.a.ch

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + 2 q^{4} - 3 q^{7} + 2 q^{11} - q^{13} - 6 q^{14} - 4 q^{16} - 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.