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SageMath
E = EllipticCurve("jk1")
E.isogeny_class()
Elliptic curves in class 100800jk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 100800.bm1 | 100800jk1 | \([0, 0, 0, -8198700, -9016254000]\) | \(551105805571803/1376829440\) | \(152266321428480000000\) | \([2]\) | \(5160960\) | \(2.7500\) | \(\Gamma_0(N)\)-optimal |
| 100800.bm2 | 100800jk2 | \([0, 0, 0, -5126700, -15854526000]\) | \(-134745327251163/903920796800\) | \(-99966408759705600000000\) | \([2]\) | \(10321920\) | \(3.0966\) |
Rank
sage: E.rank()
The elliptic curves in class 100800jk have rank \(0\).
Complex multiplication
The elliptic curves in class 100800jk do not have complex multiplication.Modular form 100800.2.a.jk
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.
