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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 326740f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
326740.f1 | 326740f1 | \([0, 0, 0, -26908, -1698087]\) | \(151732224/85\) | \(1207005006160\) | \([2]\) | \(711360\) | \(1.2654\) | \(\Gamma_0(N)\)-optimal |
326740.f2 | 326740f2 | \([0, 0, 0, -22103, -2323698]\) | \(-5256144/7225\) | \(-1641526808377600\) | \([2]\) | \(1422720\) | \(1.6120\) |
Rank
sage: E.rank()
The elliptic curves in class 326740f have rank \(1\).
Complex multiplication
The elliptic curves in class 326740f do not have complex multiplication.Modular form 326740.2.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.