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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 10830.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10830.bb1 | 10830ba2 | \([1, 0, 0, -31956, -2203830]\) | \(-27692833539889/35156250\) | \(-4581597656250\) | \([]\) | \(38880\) | \(1.3377\) | |
10830.bb2 | 10830ba1 | \([1, 0, 0, 534, -14004]\) | \(129205871/729000\) | \(-95004009000\) | \([3]\) | \(12960\) | \(0.78844\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10830.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 10830.bb do not have complex multiplication.Modular form 10830.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.