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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 56784ch
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 56784.d2 | 56784ch1 | \([0, -1, 0, 763, -92691]\) | \(5451776/413343\) | \(-3719637282816\) | \([]\) | \(96000\) | \(1.0916\) | \(\Gamma_0(N)\)-optimal |
| 56784.d1 | 56784ch2 | \([0, -1, 0, -1028837, -401325939]\) | \(-13383627864961024/151263\) | \(-1361202425856\) | \([]\) | \(480000\) | \(1.8963\) |
Rank
sage: E.rank()
The elliptic curves in class 56784ch have rank \(0\).
Complex multiplication
The elliptic curves in class 56784ch do not have complex multiplication.Modular form 56784.2.a.ch
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.
