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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 54208ch
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54208.l2 | 54208ch1 | \([0, 1, 0, 807, -6041]\) | \(8000/7\) | \(-50794196992\) | \([2]\) | \(40960\) | \(0.74175\) | \(\Gamma_0(N)\)-optimal |
| 54208.l1 | 54208ch2 | \([0, 1, 0, -4033, -57345]\) | \(125000/49\) | \(2844475031552\) | \([2]\) | \(81920\) | \(1.0883\) |
Rank
sage: E.rank()
The elliptic curves in class 54208ch have rank \(1\).
Complex multiplication
The elliptic curves in class 54208ch do not have complex multiplication.Modular form 54208.2.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.
