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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 91200f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
91200.dh2 | 91200f1 | \([0, -1, 0, -125633, -60076863]\) | \(-53540005609/350208000\) | \(-1434451968000000000\) | \([2]\) | \(1548288\) | \(2.1674\) | \(\Gamma_0(N)\)-optimal |
91200.dh1 | 91200f2 | \([0, -1, 0, -3197633, -2195116863]\) | \(882774443450089/2166000000\) | \(8871936000000000000\) | \([2]\) | \(3096576\) | \(2.5140\) |
Rank
sage: E.rank()
The elliptic curves in class 91200f have rank \(1\).
Complex multiplication
The elliptic curves in class 91200f do not have complex multiplication.Modular form 91200.2.a.f
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.