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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 270480.ch
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 270480.ch1 | 270480ch1 | \([0, -1, 0, -192096, 31000320]\) | \(1626794704081/83462400\) | \(40219721308569600\) | \([2]\) | \(3538944\) | \(1.9440\) | \(\Gamma_0(N)\)-optimal |
| 270480.ch2 | 270480ch2 | \([0, -1, 0, 121504, 122069760]\) | \(411664745519/13605414480\) | \(-6556317319813201920\) | \([2]\) | \(7077888\) | \(2.2906\) |
Rank
sage: E.rank()
The elliptic curves in class 270480.ch have rank \(1\).
Complex multiplication
The elliptic curves in class 270480.ch do not have complex multiplication.Modular form 270480.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
