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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 330330.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 330330.m1 | 330330m3 | \([1, 1, 0, -67955408468, 6818398030477488]\) | \(19590236683225255317943875248929/54195348396489300000\) | \(96010365600632980797300000\) | \([2]\) | \(884736000\) | \(4.6437\) | |
| 330330.m2 | 330330m4 | \([1, 1, 0, -5577139988, 34310839172592]\) | \(10829346205367046227129003809/5979872213745117187500000\) | \(10593708398854513549804687500000\) | \([2]\) | \(884736000\) | \(4.6437\) | |
| 330330.m3 | 330330m2 | \([1, 1, 0, -4248908468, 106446827377488]\) | \(4788502600127122071579248929/7954695558810000000000\) | \(14092228418861002410000000000\) | \([2, 2]\) | \(442368000\) | \(4.2971\) | |
| 330330.m4 | 330330m1 | \([1, 1, 0, -184237748, 2700984854352]\) | \(-390394287570401650575649/1553162059549900800000\) | \(-2751521331378281811148800000\) | \([2]\) | \(221184000\) | \(3.9505\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 330330.m have rank \(0\).
Complex multiplication
The elliptic curves in class 330330.m do not have complex multiplication.Modular form 330330.2.a.m
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.
