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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 309442e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
309442.e2 | 309442e1 | \([1, -1, 0, 427253693, 1724674077909]\) | \(9718763732247834696375/7072327531706974208\) | \(-6276716717627583822972059648\) | \([2]\) | \(145981440\) | \(4.0222\) | \(\Gamma_0(N)\)-optimal |
309442.e1 | 309442e2 | \([1, -1, 0, -1936960067, 14628079937237]\) | \(905556497427272537015625/419898849662109966848\) | \(372661774722788201804387967488\) | \([2]\) | \(291962880\) | \(4.3688\) |
Rank
sage: E.rank()
The elliptic curves in class 309442e have rank \(0\).
Complex multiplication
The elliptic curves in class 309442e do not have complex multiplication.Modular form 309442.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.