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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 229320.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 229320.ba1 | 229320dv1 | \([0, 0, 0, -5963643, 5605479558]\) | \(267080942160036/1990625\) | \(174825661046400000\) | \([2]\) | \(6881280\) | \(2.4845\) | \(\Gamma_0(N)\)-optimal |
| 229320.ba2 | 229320dv2 | \([0, 0, 0, -5840163, 5848710462]\) | \(-125415986034978/11552734375\) | \(-2029226422860000000000\) | \([2]\) | \(13762560\) | \(2.8311\) |
Rank
sage: E.rank()
The elliptic curves in class 229320.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 229320.ba do not have complex multiplication.Modular form 229320.2.a.ba
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.
