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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 194688.by
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 194688.by1 | 194688cs2 | \([0, 0, 0, -20280, -913952]\) | \(16000/3\) | \(172953293340672\) | \([2]\) | \(491520\) | \(1.4499\) | |
| 194688.by2 | 194688cs1 | \([0, 0, 0, 2535, -83486]\) | \(4000/9\) | \(-4053592812672\) | \([2]\) | \(245760\) | \(1.1033\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 194688.by have rank \(0\).
Complex multiplication
The elliptic curves in class 194688.by do not have complex multiplication.Modular form 194688.2.a.by
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.
