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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 26640z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 26640.bo2 | 26640z1 | \([0, 0, 0, -5427, 186354]\) | \(-219256227/59200\) | \(-4772796825600\) | \([2]\) | \(41472\) | \(1.1491\) | \(\Gamma_0(N)\)-optimal |
| 26640.bo1 | 26640z2 | \([0, 0, 0, -91827, 10709874]\) | \(1062144635427/54760\) | \(4414837063680\) | \([2]\) | \(82944\) | \(1.4957\) |
Rank
sage: E.rank()
The elliptic curves in class 26640z have rank \(0\).
Complex multiplication
The elliptic curves in class 26640z do not have complex multiplication.Modular form 26640.2.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 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.
