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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 56784.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 56784.q1 | 56784bn1 | \([0, -1, 0, -173, -612]\) | \(16384000/3969\) | \(139518288\) | \([2]\) | \(18432\) | \(0.27373\) | \(\Gamma_0(N)\)-optimal |
| 56784.q2 | 56784bn2 | \([0, -1, 0, 412, -4356]\) | \(13718000/21609\) | \(-12153593088\) | \([2]\) | \(36864\) | \(0.62030\) |
Rank
sage: E.rank()
The elliptic curves in class 56784.q have rank \(1\).
Complex multiplication
The elliptic curves in class 56784.q do not have complex multiplication.Modular form 56784.2.a.q
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
