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SageMath
E = EllipticCurve("ib1")
E.isogeny_class()
Elliptic curves in class 485100ib
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 485100.ib1 | 485100ib1 | \([0, 0, 0, -2752575, 1771337750]\) | \(-3704530032/33275\) | \(-20716965353700000000\) | \([]\) | \(13934592\) | \(2.5297\) | \(\Gamma_0(N)\)-optimal |
| 485100.ib2 | 485100ib2 | \([0, 0, 0, 8566425, 9351294750]\) | \(153174672/171875\) | \(-78009647432062500000000\) | \([]\) | \(41803776\) | \(3.0791\) |
Rank
sage: E.rank()
The elliptic curves in class 485100ib have rank \(1\).
Complex multiplication
The elliptic curves in class 485100ib do not have complex multiplication.Modular form 485100.2.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.
