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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 9408ch
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9408.b2 | 9408ch1 | \([0, -1, 0, 7775, 5624641]\) | \(4913/1296\) | \(-13709678915616768\) | \([2]\) | \(86016\) | \(1.7756\) | \(\Gamma_0(N)\)-optimal |
9408.b1 | 9408ch2 | \([0, -1, 0, -431265, 106164801]\) | \(838561807/26244\) | \(277620998041239552\) | \([2]\) | \(172032\) | \(2.1222\) |
Rank
sage: E.rank()
The elliptic curves in class 9408ch have rank \(1\).
Complex multiplication
The elliptic curves in class 9408ch do not have complex multiplication.Modular form 9408.2.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 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.