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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 7056.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7056.f1 | 7056bo2 | \([0, 0, 0, -62769, -6052921]\) | \(406749952\) | \(67240638864\) | \([]\) | \(15120\) | \(1.3172\) | |
| 7056.f2 | 7056bo1 | \([0, 0, 0, -1029, -2401]\) | \(1792\) | \(67240638864\) | \([]\) | \(5040\) | \(0.76792\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7056.f have rank \(1\).
Complex multiplication
The elliptic curves in class 7056.f do not have complex multiplication.Modular form 7056.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
