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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 127296di
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
127296.e2 | 127296di1 | \([0, 0, 0, -1992, 25400]\) | \(1171019776/304317\) | \(227171423232\) | \([2]\) | \(131072\) | \(0.88813\) | \(\Gamma_0(N)\)-optimal |
127296.e1 | 127296di2 | \([0, 0, 0, -29532, 1953200]\) | \(238481570896/25857\) | \(308834353152\) | \([2]\) | \(262144\) | \(1.2347\) |
Rank
sage: E.rank()
The elliptic curves in class 127296di have rank \(2\).
Complex multiplication
The elliptic curves in class 127296di do not have complex multiplication.Modular form 127296.2.a.di
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.