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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 435600bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
435600.bc2 | 435600bc1 | \([0, 0, 0, -16335, -1796850]\) | \(-432\) | \(-1115828325216000\) | \([2]\) | \(1966080\) | \(1.5757\) | \(\Gamma_0(N)\)-optimal* |
435600.bc1 | 435600bc2 | \([0, 0, 0, -343035, -77264550]\) | \(1000188\) | \(4463313300864000\) | \([2]\) | \(3932160\) | \(1.9223\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 435600bc have rank \(1\).
Complex multiplication
The elliptic curves in class 435600bc do not have complex multiplication.Modular form 435600.2.a.bc
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.