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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 142912bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 142912.be2 | 142912bx1 | \([0, 0, 0, -15020, -5647696]\) | \(-5718124138500/206945952367\) | \(-13562409934323712\) | \([2]\) | \(573440\) | \(1.7757\) | \(\Gamma_0(N)\)-optimal |
| 142912.be1 | 142912bx2 | \([0, 0, 0, -576460, -167566992]\) | \(161629756274927250/991205648741\) | \(129919306791780352\) | \([2]\) | \(1146880\) | \(2.1223\) |
Rank
sage: E.rank()
The elliptic curves in class 142912bx have rank \(0\).
Complex multiplication
The elliptic curves in class 142912bx do not have complex multiplication.Modular form 142912.2.a.bx
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.
