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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)
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.