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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 14450.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14450.g1 | 14450h1 | \([1, 1, 0, -289150, 74712500]\) | \(-24529249/8000\) | \(-871969680125000000\) | \([]\) | \(176256\) | \(2.1550\) | \(\Gamma_0(N)\)-optimal |
14450.g2 | 14450h2 | \([1, 1, 0, 2167350, -679433000]\) | \(10329972191/7812500\) | \(-851532890747070312500\) | \([]\) | \(528768\) | \(2.7043\) |
Rank
sage: E.rank()
The elliptic curves in class 14450.g have rank \(0\).
Complex multiplication
The elliptic curves in class 14450.g do not have complex multiplication.Modular form 14450.2.a.g
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.