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SageMath
sage: E = EllipticCurve("b1")
sage: E.isogeny_class()
Elliptic curves in class 1248b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1248.d2 | 1248b1 | \([0, -1, 0, -98, -132]\) | \(1643032000/767637\) | \(49128768\) | \([2]\) | \(320\) | \(0.17024\) | \(\Gamma_0(N)\)-optimal |
| 1248.d1 | 1248b2 | \([0, -1, 0, -1313, -17871]\) | \(61162984000/41067\) | \(168210432\) | \([2]\) | \(640\) | \(0.51681\) |
Rank
sage: E.rank()
The elliptic curves in class 1248b have rank \(0\).
Complex multiplication
The elliptic curves in class 1248b do not have complex multiplication.Modular form 1248.2.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 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.
