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SageMath
E = EllipticCurve("dl1")
E.isogeny_class()
Elliptic curves in class 105840dl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 105840.dc1 | 105840dl1 | \([0, 0, 0, -124803, 16973698]\) | \(-16522921323/4000\) | \(-52044152832000\) | \([]\) | \(518400\) | \(1.6207\) | \(\Gamma_0(N)\)-optimal |
| 105840.dc2 | 105840dl2 | \([0, 0, 0, 51597, 59807538]\) | \(1601613/163840\) | \(-1554030076499066880\) | \([]\) | \(1555200\) | \(2.1700\) |
Rank
sage: E.rank()
The elliptic curves in class 105840dl have rank \(1\).
Complex multiplication
The elliptic curves in class 105840dl do not have complex multiplication.Modular form 105840.2.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 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.
