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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 143472j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 143472.bu2 | 143472j1 | \([0, 1, 0, -3936, 732276]\) | \(-13997521/474336\) | \(-228577919238144\) | \([]\) | \(518400\) | \(1.4355\) | \(\Gamma_0(N)\)-optimal |
| 143472.bu1 | 143472j2 | \([0, 1, 0, -403776, -124253004]\) | \(-15107691357361/5067577806\) | \(-2442016609476993024\) | \([]\) | \(2592000\) | \(2.2403\) |
Rank
sage: E.rank()
The elliptic curves in class 143472j have rank \(2\).
Complex multiplication
The elliptic curves in class 143472j do not have complex multiplication.Modular form 143472.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
