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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 229320.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 229320.a1 | 229320dp1 | \([0, 0, 0, -765723, -257800858]\) | \(565357377316/257985\) | \(22657405671613440\) | \([2]\) | \(3538944\) | \(2.0955\) | \(\Gamma_0(N)\)-optimal |
| 229320.a2 | 229320dp2 | \([0, 0, 0, -642243, -343718242]\) | \(-166792350818/194041575\) | \(-34083211674584217600\) | \([2]\) | \(7077888\) | \(2.4421\) |
Rank
sage: E.rank()
The elliptic curves in class 229320.a have rank \(1\).
Complex multiplication
The elliptic curves in class 229320.a do not have complex multiplication.Modular form 229320.2.a.a
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.
