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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 350064z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 350064.z1 | 350064z1 | \([0, 0, 0, -4260, -102269]\) | \(733001728000/36822357\) | \(429495972048\) | \([2]\) | \(344064\) | \(0.99075\) | \(\Gamma_0(N)\)-optimal |
| 350064.z2 | 350064z2 | \([0, 0, 0, 2625, -401078]\) | \(10718750000/378572337\) | \(-70650683820288\) | \([2]\) | \(688128\) | \(1.3373\) |
Rank
sage: E.rank()
The elliptic curves in class 350064z have rank \(1\).
Complex multiplication
The elliptic curves in class 350064z do not have complex multiplication.Modular form 350064.2.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.
