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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 10830.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10830.z1 | 10830bb2 | \([1, 0, 0, -25781, 1590945]\) | \(276288773643091/41990400\) | \(288012153600\) | \([2]\) | \(20480\) | \(1.2114\) | |
| 10830.z2 | 10830bb1 | \([1, 0, 0, -1461, 29601]\) | \(-50284268371/26542080\) | \(-182052126720\) | \([2]\) | \(10240\) | \(0.86482\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10830.z have rank \(1\).
Complex multiplication
The elliptic curves in class 10830.z do not have complex multiplication.Modular form 10830.2.a.z
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.
