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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 18480.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18480.g1 | 18480br3 | \([0, -1, 0, -13816, 624880]\) | \(71210194441849/631496250\) | \(2586608640000\) | \([2]\) | \(49152\) | \(1.2051\) | |
| 18480.g2 | 18480br2 | \([0, -1, 0, -1496, -5904]\) | \(90458382169/48024900\) | \(196709990400\) | \([2, 2]\) | \(24576\) | \(0.85851\) | |
| 18480.g3 | 18480br1 | \([0, -1, 0, -1176, -15120]\) | \(43949604889/55440\) | \(227082240\) | \([2]\) | \(12288\) | \(0.51194\) | \(\Gamma_0(N)\)-optimal |
| 18480.g4 | 18480br4 | \([0, -1, 0, 5704, -51984]\) | \(5009866738631/3163773690\) | \(-12958817034240\) | \([2]\) | \(49152\) | \(1.2051\) |
Rank
sage: E.rank()
The elliptic curves in class 18480.g have rank \(1\).
Complex multiplication
The elliptic curves in class 18480.g do not have complex multiplication.Modular form 18480.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
