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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 855.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 855.b1 | 855b2 | \([1, -1, 1, -842, 9366]\) | \(90458382169/2671875\) | \(1947796875\) | \([2]\) | \(384\) | \(0.55965\) | |
| 855.b2 | 855b1 | \([1, -1, 1, 13, 474]\) | \(357911/135375\) | \(-98688375\) | \([2]\) | \(192\) | \(0.21307\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 855.b have rank \(1\).
Complex multiplication
The elliptic curves in class 855.b do not have complex multiplication.Modular form 855.2.a.b
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.
