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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 72128.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
72128.f1 | 72128cg2 | \([0, 1, 0, -1105505, -447761441]\) | \(38758598383688/25921\) | \(99928628559872\) | \([2]\) | \(1376256\) | \(2.0026\) | |
72128.f2 | 72128cg1 | \([0, 1, 0, -68665, -7104441]\) | \(-74299881664/1958887\) | \(-943968651931648\) | \([2]\) | \(688128\) | \(1.6560\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 72128.f have rank \(0\).
Complex multiplication
The elliptic curves in class 72128.f do not have complex multiplication.Modular form 72128.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.