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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 108900.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
108900.bb1 | 108900ce2 | \([0, 0, 0, -10790175, -13638424250]\) | \(26894628304/9075\) | \(46880287274700000000\) | \([2]\) | \(4423680\) | \(2.7466\) | |
108900.bb2 | 108900ce1 | \([0, 0, 0, -580800, -274352375]\) | \(-67108864/61875\) | \(-19977395145468750000\) | \([2]\) | \(2211840\) | \(2.4001\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 108900.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 108900.bb do not have complex multiplication.Modular form 108900.2.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 LMFDB 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 LMFDB labels.