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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 39600.db
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39600.db1 | 39600ds2 | \([0, 0, 0, -17175, 859250]\) | \(192143824/1815\) | \(5292540000000\) | \([2]\) | \(73728\) | \(1.2622\) | |
39600.db2 | 39600ds1 | \([0, 0, 0, -300, 32375]\) | \(-16384/2475\) | \(-451068750000\) | \([2]\) | \(36864\) | \(0.91562\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 39600.db have rank \(0\).
Complex multiplication
The elliptic curves in class 39600.db do not have complex multiplication.Modular form 39600.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.