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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 46800db
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46800.cj3 | 46800db1 | \([0, 0, 0, 1725, 45250]\) | \(12167/26\) | \(-1213056000000\) | \([]\) | \(51840\) | \(1.0029\) | \(\Gamma_0(N)\)-optimal |
| 46800.cj2 | 46800db2 | \([0, 0, 0, -16275, -1592750]\) | \(-10218313/17576\) | \(-820025856000000\) | \([]\) | \(155520\) | \(1.5523\) | |
| 46800.cj1 | 46800db3 | \([0, 0, 0, -1654275, -818954750]\) | \(-10730978619193/6656\) | \(-310542336000000\) | \([]\) | \(466560\) | \(2.1016\) |
Rank
sage: E.rank()
The elliptic curves in class 46800db have rank \(1\).
Complex multiplication
The elliptic curves in class 46800db do not have complex multiplication.Modular form 46800.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
