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SageMath
E = EllipticCurve("ib1")
E.isogeny_class()
Elliptic curves in class 388080ib
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.ib2 | 388080ib1 | \([0, 0, 0, 35133, 1209026]\) | \(668944031/475200\) | \(-3406873971916800\) | \([]\) | \(2322432\) | \(1.6688\) | \(\Gamma_0(N)\)-optimal |
| 388080.ib1 | 388080ib2 | \([0, 0, 0, -388227, -113182846]\) | \(-902612375329/249562500\) | \(-1789200306432000000\) | \([]\) | \(6967296\) | \(2.2181\) |
Rank
sage: E.rank()
The elliptic curves in class 388080ib have rank \(0\).
Complex multiplication
The elliptic curves in class 388080ib do not have complex multiplication.Modular form 388080.2.a.ib
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
