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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 31200o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 31200.cf2 | 31200o1 | \([0, 1, 0, -458, 3588]\) | \(10648000/117\) | \(117000000\) | \([2]\) | \(9216\) | \(0.36283\) | \(\Gamma_0(N)\)-optimal |
| 31200.cf1 | 31200o2 | \([0, 1, 0, -833, -3537]\) | \(1000000/507\) | \(32448000000\) | \([2]\) | \(18432\) | \(0.70940\) |
Rank
sage: E.rank()
The elliptic curves in class 31200o have rank \(0\).
Complex multiplication
The elliptic curves in class 31200o do not have complex multiplication.Modular form 31200.2.a.o
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.
