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SageMath
E = EllipticCurve("dl1")
E.isogeny_class()
Elliptic curves in class 119952.dl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 119952.dl1 | 119952ek2 | \([0, 0, 0, -846496560, 9479548208284]\) | \(-1272481306550272000/5865429267\) | \(-309205845521751654427392\) | \([]\) | \(24675840\) | \(3.7107\) | |
| 119952.dl2 | 119952ek1 | \([0, 0, 0, -6338640, 23318771308]\) | \(-534274048000/4146834123\) | \(-218607248143747242517248\) | \([]\) | \(8225280\) | \(3.1614\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 119952.dl have rank \(0\).
Complex multiplication
The elliptic curves in class 119952.dl do not have complex multiplication.Modular form 119952.2.a.dl
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
