Show commands:
SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 230640.bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 230640.bx1 | 230640bx4 | \([0, 1, 0, -9771002416, -371758221299116]\) | \(28379906689597370652529/1357352437500\) | \(4934268046113064704000000\) | \([2]\) | \(199065600\) | \(4.2155\) | |
| 230640.bx2 | 230640bx3 | \([0, 1, 0, -609674096, -5829116479020]\) | \(-6894246873502147249/47925198774000\) | \(-174218405169486590337024000\) | \([2]\) | \(99532800\) | \(3.8689\) | |
| 230640.bx3 | 230640bx2 | \([0, 1, 0, -131172976, -415581142060]\) | \(68663623745397169/19216056254400\) | \(69854497423700264740454400\) | \([2]\) | \(66355200\) | \(3.6662\) | |
| 230640.bx4 | 230640bx1 | \([0, 1, 0, 21356944, -42614981676]\) | \(296354077829711/387386634240\) | \(-1408233733563189810954240\) | \([2]\) | \(33177600\) | \(3.3196\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 230640.bx have rank \(0\).
Complex multiplication
The elliptic curves in class 230640.bx do not have complex multiplication.Modular form 230640.2.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 LMFDB 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 LMFDB labels.
