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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 156702bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 156702.w2 | 156702bx1 | \([1, 0, 1, -432, -4994]\) | \(-25908060079/15964416\) | \(-5475794688\) | \([2]\) | \(110592\) | \(0.57051\) | \(\Gamma_0(N)\)-optimal |
| 156702.w1 | 156702bx2 | \([1, 0, 1, -7712, -261250]\) | \(147859659147439/28321488\) | \(9714270384\) | \([2]\) | \(221184\) | \(0.91708\) |
Rank
sage: E.rank()
The elliptic curves in class 156702bx have rank \(1\).
Complex multiplication
The elliptic curves in class 156702bx do not have complex multiplication.Modular form 156702.2.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.
