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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 11271a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11271.b2 | 11271a1 | \([1, 1, 1, -9543, -344196]\) | \(3981876625/232713\) | \(5617126094697\) | \([2]\) | \(18432\) | \(1.1999\) | \(\Gamma_0(N)\)-optimal |
| 11271.b1 | 11271a2 | \([1, 1, 1, -28328, 1399052]\) | \(104154702625/24649677\) | \(594983279415213\) | \([2]\) | \(36864\) | \(1.5465\) |
Rank
sage: E.rank()
The elliptic curves in class 11271a have rank \(1\).
Complex multiplication
The elliptic curves in class 11271a do not have complex multiplication.Modular form 11271.2.a.a
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.
