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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 2448f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2448.j2 | 2448f1 | \([0, 0, 0, -75, -182]\) | \(62500/17\) | \(12690432\) | \([2]\) | \(384\) | \(0.070888\) | \(\Gamma_0(N)\)-optimal |
2448.j1 | 2448f2 | \([0, 0, 0, -435, 3346]\) | \(6097250/289\) | \(431474688\) | \([2]\) | \(768\) | \(0.41746\) |
Rank
sage: E.rank()
The elliptic curves in class 2448f have rank \(1\).
Complex multiplication
The elliptic curves in class 2448f do not have complex multiplication.Modular form 2448.2.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.