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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 5202l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5202.g1 | 5202l1 | \([1, -1, 1, -6557, -128095]\) | \(1771561/612\) | \(10768928134212\) | \([2]\) | \(18432\) | \(1.2024\) | \(\Gamma_0(N)\)-optimal |
5202.g2 | 5202l2 | \([1, -1, 1, 19453, -908395]\) | \(46268279/46818\) | \(-823823002267218\) | \([2]\) | \(36864\) | \(1.5490\) |
Rank
sage: E.rank()
The elliptic curves in class 5202l have rank \(1\).
Complex multiplication
The elliptic curves in class 5202l do not have complex multiplication.Modular form 5202.2.a.l
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.