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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 110400bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
110400.dl2 | 110400bc1 | \([0, -1, 0, -36444033, -5813912232063]\) | \(-1306902141891515161/3564268498800000000\) | \(-14599243771084800000000000000\) | \([2]\) | \(79626240\) | \(4.0832\) | \(\Gamma_0(N)\)-optimal |
110400.dl1 | 110400bc2 | \([0, -1, 0, -5075292033, -137423583144063]\) | \(3529773792266261468365081/50841342773437500000\) | \(208246140000000000000000000000\) | \([2]\) | \(159252480\) | \(4.4298\) |
Rank
sage: E.rank()
The elliptic curves in class 110400bc have rank \(0\).
Complex multiplication
The elliptic curves in class 110400bc do not have complex multiplication.Modular form 110400.2.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.