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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 57222x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57222.bd1 | 57222x1 | \([1, -1, 0, -509850, 140162548]\) | \(832972004929/610368\) | \(10740210992520768\) | \([2]\) | \(884736\) | \(2.0103\) | \(\Gamma_0(N)\)-optimal |
| 57222.bd2 | 57222x2 | \([1, -1, 0, -405810, 198945148]\) | \(-420021471169/727634952\) | \(-12803674029458820552\) | \([2]\) | \(1769472\) | \(2.3569\) |
Rank
sage: E.rank()
The elliptic curves in class 57222x have rank \(1\).
Complex multiplication
The elliptic curves in class 57222x do not have complex multiplication.Modular form 57222.2.a.x
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.
