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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 1800.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1800.q1 | 1800v2 | \([0, 0, 0, -1515, 14150]\) | \(2060602/729\) | \(136048896000\) | \([2]\) | \(1536\) | \(0.83751\) | |
1800.q2 | 1800v1 | \([0, 0, 0, 285, 1550]\) | \(27436/27\) | \(-2519424000\) | \([2]\) | \(768\) | \(0.49093\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1800.q have rank \(0\).
Complex multiplication
The elliptic curves in class 1800.q do not have complex multiplication.Modular form 1800.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.