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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 350727f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
350727.f2 | 350727f1 | \([1, 0, 0, -17468, 841095]\) | \(3981876625/232713\) | \(34449875836857\) | \([2]\) | \(720896\) | \(1.3511\) | \(\Gamma_0(N)\)-optimal |
350727.f1 | 350727f2 | \([1, 0, 0, -51853, -3498292]\) | \(104154702625/24649677\) | \(3649036848257853\) | \([2]\) | \(1441792\) | \(1.6976\) |
Rank
sage: E.rank()
The elliptic curves in class 350727f have rank \(1\).
Complex multiplication
The elliptic curves in class 350727f do not have complex multiplication.Modular form 350727.2.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.