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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 67600db
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
67600.z2 | 67600db1 | \([0, -1, 0, -225333, -38168963]\) | \(163840/13\) | \(100397627200000000\) | \([]\) | \(725760\) | \(2.0059\) | \(\Gamma_0(N)\)-optimal |
67600.z1 | 67600db2 | \([0, -1, 0, -3605333, 2628651037]\) | \(671088640/2197\) | \(16967198996800000000\) | \([]\) | \(2177280\) | \(2.5552\) |
Rank
sage: E.rank()
The elliptic curves in class 67600db have rank \(1\).
Complex multiplication
The elliptic curves in class 67600db do not have complex multiplication.Modular form 67600.2.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 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.