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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 10830bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10830.z2 | 10830bb1 | \([1, 0, 0, -1461, 29601]\) | \(-50284268371/26542080\) | \(-182052126720\) | \([2]\) | \(10240\) | \(0.86482\) | \(\Gamma_0(N)\)-optimal |
10830.z1 | 10830bb2 | \([1, 0, 0, -25781, 1590945]\) | \(276288773643091/41990400\) | \(288012153600\) | \([2]\) | \(20480\) | \(1.2114\) |
Rank
sage: E.rank()
The elliptic curves in class 10830bb have rank \(1\).
Complex multiplication
The elliptic curves in class 10830bb 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 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.