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SageMath
E = EllipticCurve("po1")
E.isogeny_class()
Elliptic curves in class 310464.po
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
310464.po1 | 310464po1 | \([0, 0, 0, -936684, -348658128]\) | \(598885164/539\) | \(81799044065722368\) | \([2]\) | \(4128768\) | \(2.1697\) | \(\Gamma_0(N)\)-optimal |
310464.po2 | 310464po2 | \([0, 0, 0, -725004, -510466320]\) | \(-138853062/290521\) | \(-88179369502848712704\) | \([2]\) | \(8257536\) | \(2.5162\) |
Rank
sage: E.rank()
The elliptic curves in class 310464.po have rank \(1\).
Complex multiplication
The elliptic curves in class 310464.po do not have complex multiplication.Modular form 310464.2.a.po
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.