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SageMath
E = EllipticCurve("gl1")
E.isogeny_class()
Elliptic curves in class 66150.gl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
66150.gl1 | 66150go1 | \([1, -1, 1, -195005, -33103003]\) | \(-16522921323/4000\) | \(-198532687500000\) | \([]\) | \(518400\) | \(1.7323\) | \(\Gamma_0(N)\)-optimal |
66150.gl2 | 66150go2 | \([1, -1, 1, 80620, -116831753]\) | \(1601613/163840\) | \(-5928154283520000000\) | \([]\) | \(1555200\) | \(2.2816\) |
Rank
sage: E.rank()
The elliptic curves in class 66150.gl have rank \(1\).
Complex multiplication
The elliptic curves in class 66150.gl do not have complex multiplication.Modular form 66150.2.a.gl
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.