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SageMath
E = EllipticCurve("dj1")
E.isogeny_class()
Elliptic curves in class 141570dj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141570.cj2 | 141570dj1 | \([1, -1, 0, 763416, -367939962]\) | \(557820238477845431/985142146218750\) | \(-86898403575809718750\) | \([]\) | \(6220800\) | \(2.5108\) | \(\Gamma_0(N)\)-optimal |
| 141570.cj1 | 141570dj2 | \([1, -1, 0, -25819569, -50685777675]\) | \(-21580315425730848803929/96405029296875000\) | \(-8503791229248046875000\) | \([]\) | \(18662400\) | \(3.0601\) |
Rank
sage: E.rank()
The elliptic curves in class 141570dj have rank \(0\).
Complex multiplication
The elliptic curves in class 141570dj do not have complex multiplication.Modular form 141570.2.a.dj
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
