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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 72432.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 72432.v1 | 72432bo2 | \([0, 0, 0, -4635, 27594]\) | \(3687953625/2024072\) | \(6043846606848\) | \([2]\) | \(96768\) | \(1.1432\) | |
| 72432.v2 | 72432bo1 | \([0, 0, 0, 1125, 3402]\) | \(52734375/32192\) | \(-96124796928\) | \([2]\) | \(48384\) | \(0.79660\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 72432.v have rank \(0\).
Complex multiplication
The elliptic curves in class 72432.v do not have complex multiplication.Modular form 72432.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
