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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 45486o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 45486.b1 | 45486o1 | \([1, -1, 0, -394821, -161470827]\) | \(-549754417/592704\) | \(-7338278570767937856\) | \([]\) | \(984960\) | \(2.3149\) | \(\Gamma_0(N)\)-optimal |
| 45486.b2 | 45486o2 | \([1, -1, 0, 3309039, 2916436833]\) | \(323648023823/484243284\) | \(-5995424552585257783476\) | \([3]\) | \(2954880\) | \(2.8642\) |
Rank
sage: E.rank()
The elliptic curves in class 45486o have rank \(1\).
Complex multiplication
The elliptic curves in class 45486o do not have complex multiplication.Modular form 45486.2.a.o
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
