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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 25350bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25350.cl3 | 25350bx1 | \([1, 1, 1, -25438, 10013531]\) | \(-24137569/561600\) | \(-42355248975000000\) | \([2]\) | \(193536\) | \(1.8711\) | \(\Gamma_0(N)\)-optimal |
| 25350.cl2 | 25350bx2 | \([1, 1, 1, -870438, 310833531]\) | \(967068262369/4928040\) | \(371667309755625000\) | \([2]\) | \(387072\) | \(2.2177\) | |
| 25350.cl4 | 25350bx3 | \([1, 1, 1, 228062, -264780469]\) | \(17394111071/411937500\) | \(-31067869256835937500\) | \([2]\) | \(580608\) | \(2.4204\) | |
| 25350.cl1 | 25350bx4 | \([1, 1, 1, -5053188, -4151780469]\) | \(189208196468929/10860320250\) | \(819073305087222656250\) | \([2]\) | \(1161216\) | \(2.7670\) |
Rank
sage: E.rank()
The elliptic curves in class 25350bx have rank \(0\).
Complex multiplication
The elliptic curves in class 25350bx do not have complex multiplication.Modular form 25350.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
