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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 78400.di
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
78400.di1 | 78400ge2 | \([0, -1, 0, -697433, 224414737]\) | \(406749952\) | \(92236816000000\) | \([]\) | \(435456\) | \(1.9192\) | |
78400.di2 | 78400ge1 | \([0, -1, 0, -11433, 92737]\) | \(1792\) | \(92236816000000\) | \([]\) | \(145152\) | \(1.3699\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 78400.di have rank \(0\).
Complex multiplication
The elliptic curves in class 78400.di do not have complex multiplication.Modular form 78400.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.