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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 44400bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44400.ba2 | 44400bc1 | \([0, -1, 0, -458408, 188787312]\) | \(-166456688365729/143856000000\) | \(-9206784000000000000\) | \([2]\) | \(691200\) | \(2.3363\) | \(\Gamma_0(N)\)-optimal |
44400.ba1 | 44400bc2 | \([0, -1, 0, -8458408, 9468787312]\) | \(1045706191321645729/323352324000\) | \(20694548736000000000\) | \([2]\) | \(1382400\) | \(2.6829\) |
Rank
sage: E.rank()
The elliptic curves in class 44400bc have rank \(1\).
Complex multiplication
The elliptic curves in class 44400bc do not have complex multiplication.Modular form 44400.2.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.