Show commands:
SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 141960.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141960.bg1 | 141960bw4 | \([0, -1, 0, -4221000, -3336471828]\) | \(841356017734178/1404585\) | \(13884750887454720\) | \([2]\) | \(3440640\) | \(2.3596\) | |
| 141960.bg2 | 141960bw3 | \([0, -1, 0, -692280, 153261900]\) | \(3711757787138/1124589375\) | \(11116908782703360000\) | \([2]\) | \(3440640\) | \(2.3596\) | |
| 141960.bg3 | 141960bw2 | \([0, -1, 0, -266400, -50990148]\) | \(423026849956/16769025\) | \(82883461930214400\) | \([2, 2]\) | \(1720320\) | \(2.0131\) | |
| 141960.bg4 | 141960bw1 | \([0, -1, 0, 7380, -2914380]\) | \(35969456/2985255\) | \(-3688769459531520\) | \([2]\) | \(860160\) | \(1.6665\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141960.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 141960.bg do not have complex multiplication.Modular form 141960.2.a.bg
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
