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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 69828z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 69828.u2 | 69828z1 | \([0, 1, 0, -2516629, -1541494264]\) | \(-744208243621888/2244044979\) | \(-5315187094756021296\) | \([2]\) | \(1976832\) | \(2.4623\) | \(\Gamma_0(N)\)-optimal |
| 69828.u1 | 69828z2 | \([0, 1, 0, -40295164, -98466103660]\) | \(190930594365830608/1728243\) | \(65495549161734912\) | \([2]\) | \(3953664\) | \(2.8089\) |
Rank
sage: E.rank()
The elliptic curves in class 69828z have rank \(0\).
Complex multiplication
The elliptic curves in class 69828z do not have complex multiplication.Modular form 69828.2.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.
