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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 54080ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54080.l2 | 54080ba1 | \([0, 1, 0, -741121, -94197921]\) | \(16194277/8000\) | \(22239247069085696000\) | \([2]\) | \(1078272\) | \(2.4055\) | \(\Gamma_0(N)\)-optimal |
| 54080.l1 | 54080ba2 | \([0, 1, 0, -6365441, 6113926495]\) | \(10260751717/125000\) | \(347488235454464000000\) | \([2]\) | \(2156544\) | \(2.7520\) |
Rank
sage: E.rank()
The elliptic curves in class 54080ba have rank \(0\).
Complex multiplication
The elliptic curves in class 54080ba do not have complex multiplication.Modular form 54080.2.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 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.
