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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 4800q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4800.cb4 | 4800q1 | \([0, 1, 0, 92, 938]\) | \(85184/405\) | \(-405000000\) | \([2]\) | \(1536\) | \(0.33395\) | \(\Gamma_0(N)\)-optimal |
| 4800.cb3 | 4800q2 | \([0, 1, 0, -1033, 11063]\) | \(1906624/225\) | \(14400000000\) | \([2, 2]\) | \(3072\) | \(0.68052\) | |
| 4800.cb2 | 4800q3 | \([0, 1, 0, -4033, -87937]\) | \(14172488/1875\) | \(960000000000\) | \([2]\) | \(6144\) | \(1.0271\) | |
| 4800.cb1 | 4800q4 | \([0, 1, 0, -16033, 776063]\) | \(890277128/15\) | \(7680000000\) | \([2]\) | \(6144\) | \(1.0271\) |
Rank
sage: E.rank()
The elliptic curves in class 4800q have rank \(0\).
Complex multiplication
The elliptic curves in class 4800q do not have complex multiplication.Modular form 4800.2.a.q
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.
