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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 59290.db
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
59290.db1 | 59290em1 | \([1, 1, 1, -20875, -1171983]\) | \(-584043889/1400\) | \(-2411498612600\) | \([]\) | \(165888\) | \(1.2553\) | \(\Gamma_0(N)\)-optimal |
59290.db2 | 59290em2 | \([1, 1, 1, 38415, -5844035]\) | \(3639707951/10718750\) | \(-18463036252718750\) | \([]\) | \(497664\) | \(1.8046\) |
Rank
sage: E.rank()
The elliptic curves in class 59290.db have rank \(1\).
Complex multiplication
The elliptic curves in class 59290.db do not have complex multiplication.Modular form 59290.2.a.db
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.