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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 2700.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2700.q1 | 2700r2 | \([0, 0, 0, -138375, -19811250]\) | \(16541040\) | \(17714700000000\) | \([]\) | \(9720\) | \(1.6029\) | |
| 2700.q2 | 2700r1 | \([0, 0, 0, -3375, 33750]\) | \(2160\) | \(1968300000000\) | \([3]\) | \(3240\) | \(1.0536\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2700.q have rank \(0\).
Complex multiplication
The elliptic curves in class 2700.q do not have complex multiplication.Modular form 2700.2.a.q
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.
