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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 29302e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
29302.f2 | 29302e1 | \([1, 0, 0, 13327, -800087]\) | \(45408227375/74381632\) | \(-428795306535232\) | \([3]\) | \(127008\) | \(1.4928\) | \(\Gamma_0(N)\)-optimal |
29302.f1 | 29302e2 | \([1, 0, 0, -432573, -110009915]\) | \(-1552807715412625/7697866228\) | \(-44376666929040628\) | \([]\) | \(381024\) | \(2.0421\) |
Rank
sage: E.rank()
The elliptic curves in class 29302e have rank \(1\).
Complex multiplication
The elliptic curves in class 29302e do not have complex multiplication.Modular form 29302.2.a.e
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.