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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 53550bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 53550.j2 | 53550bd1 | \([1, -1, 0, -32667, 10184741]\) | \(-338463151209/3731840000\) | \(-42507990000000000\) | \([2]\) | \(368640\) | \(1.8727\) | \(\Gamma_0(N)\)-optimal |
| 53550.j1 | 53550bd2 | \([1, -1, 0, -932667, 345884741]\) | \(7876916680687209/27200448800\) | \(309830112112500000\) | \([2]\) | \(737280\) | \(2.2193\) |
Rank
sage: E.rank()
The elliptic curves in class 53550bd have rank \(1\).
Complex multiplication
The elliptic curves in class 53550bd do not have complex multiplication.Modular form 53550.2.a.bd
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
