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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 56784bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 56784.v2 | 56784bv1 | \([0, -1, 0, -21168, -1166400]\) | \(1515434103625/17635968\) | \(12208040312832\) | \([]\) | \(145152\) | \(1.3235\) | \(\Gamma_0(N)\)-optimal |
| 56784.v1 | 56784bv2 | \([0, -1, 0, -161568, 24420096]\) | \(673822943613625/19421724672\) | \(13444183939350528\) | \([]\) | \(435456\) | \(1.8728\) |
Rank
sage: E.rank()
The elliptic curves in class 56784bv have rank \(1\).
Complex multiplication
The elliptic curves in class 56784bv do not have complex multiplication.Modular form 56784.2.a.bv
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.
