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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 88200bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 88200.dy3 | 88200bx1 | \([0, 0, 0, -80850, -8789375]\) | \(2725888/21\) | \(450272135250000\) | \([2]\) | \(393216\) | \(1.6408\) | \(\Gamma_0(N)\)-optimal |
| 88200.dy2 | 88200bx2 | \([0, 0, 0, -135975, 4716250]\) | \(810448/441\) | \(151291437444000000\) | \([2, 2]\) | \(786432\) | \(1.9874\) | |
| 88200.dy4 | 88200bx3 | \([0, 0, 0, 525525, 37129750]\) | \(11696828/7203\) | \(-9884373913008000000\) | \([2]\) | \(1572864\) | \(2.3339\) | |
| 88200.dy1 | 88200bx4 | \([0, 0, 0, -1679475, 836662750]\) | \(381775972/567\) | \(778070249712000000\) | \([2]\) | \(1572864\) | \(2.3339\) |
Rank
sage: E.rank()
The elliptic curves in class 88200bx have rank \(1\).
Complex multiplication
The elliptic curves in class 88200bx do not have complex multiplication.Modular form 88200.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
