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SageMath
E = EllipticCurve("do1")
E.isogeny_class()
Elliptic curves in class 123200do
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 123200.eu1 | 123200do1 | \([0, 0, 0, -24940, -1515600]\) | \(52355598021/15092\) | \(494534656000\) | \([2]\) | \(221184\) | \(1.2239\) | \(\Gamma_0(N)\)-optimal |
| 123200.eu2 | 123200do2 | \([0, 0, 0, -21740, -1918800]\) | \(-34677868581/28471058\) | \(-932939628544000\) | \([2]\) | \(442368\) | \(1.5705\) |
Rank
sage: E.rank()
The elliptic curves in class 123200do have rank \(0\).
Complex multiplication
The elliptic curves in class 123200do do not have complex multiplication.Modular form 123200.2.a.do
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.
