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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 144900bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
144900.c1 | 144900bb1 | \([0, 0, 0, -2272800, -1318757375]\) | \(7124261256822784/475453125\) | \(86651332031250000\) | \([2]\) | \(3317760\) | \(2.3056\) | \(\Gamma_0(N)\)-optimal |
144900.c2 | 144900bb2 | \([0, 0, 0, -2132175, -1489054250]\) | \(-367624742361424/115740505125\) | \(-337499312944500000000\) | \([2]\) | \(6635520\) | \(2.6522\) |
Rank
sage: E.rank()
The elliptic curves in class 144900bb have rank \(1\).
Complex multiplication
The elliptic curves in class 144900bb do not have complex multiplication.Modular form 144900.2.a.bb
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.