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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 13520s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13520.z1 | 13520s1 | \([0, -1, 0, -27096, -1795600]\) | \(-658489/40\) | \(-133649321328640\) | \([]\) | \(44928\) | \(1.4654\) | \(\Gamma_0(N)\)-optimal |
13520.z2 | 13520s2 | \([0, -1, 0, 148664, -2920464]\) | \(108750551/64000\) | \(-213838914125824000\) | \([]\) | \(134784\) | \(2.0147\) |
Rank
sage: E.rank()
The elliptic curves in class 13520s have rank \(0\).
Complex multiplication
The elliptic curves in class 13520s do not have complex multiplication.Modular form 13520.2.a.s
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.