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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 97020bz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
97020.u1 | 97020bz1 | \([0, 0, 0, -273, 1757]\) | \(-3937024/55\) | \(-31434480\) | \([]\) | \(31104\) | \(0.24460\) | \(\Gamma_0(N)\)-optimal |
97020.u2 | 97020bz2 | \([0, 0, 0, 987, 8813]\) | \(186050816/166375\) | \(-95089302000\) | \([]\) | \(93312\) | \(0.79391\) |
Rank
sage: E.rank()
The elliptic curves in class 97020bz have rank \(1\).
Complex multiplication
The elliptic curves in class 97020bz do not have complex multiplication.Modular form 97020.2.a.bz
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.