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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 14450b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14450.k1 | 14450b1 | \([1, 0, 1, -1001, 15148]\) | \(-24529249/8000\) | \(-36125000000\) | \([]\) | \(10368\) | \(0.73837\) | \(\Gamma_0(N)\)-optimal |
14450.k2 | 14450b2 | \([1, 0, 1, 7499, -137852]\) | \(10329972191/7812500\) | \(-35278320312500\) | \([]\) | \(31104\) | \(1.2877\) |
Rank
sage: E.rank()
The elliptic curves in class 14450b have rank \(1\).
Complex multiplication
The elliptic curves in class 14450b do not have complex multiplication.Modular form 14450.2.a.b
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.