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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 9920j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9920.d2 | 9920j1 | \([0, 1, 0, -4225, -110625]\) | \(-31824875809/1240000\) | \(-325058560000\) | \([2]\) | \(9216\) | \(0.97809\) | \(\Gamma_0(N)\)-optimal |
| 9920.d1 | 9920j2 | \([0, 1, 0, -68225, -6881825]\) | \(133974081659809/192200\) | \(50384076800\) | \([2]\) | \(18432\) | \(1.3247\) |
Rank
sage: E.rank()
The elliptic curves in class 9920j have rank \(0\).
Complex multiplication
The elliptic curves in class 9920j do not have complex multiplication.Modular form 9920.2.a.j
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.
