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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 54150m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54150.e4 | 54150m1 | \([1, 1, 0, -1090, 18400]\) | \(-24389/12\) | \(-70568821500\) | \([2]\) | \(57600\) | \(0.78695\) | \(\Gamma_0(N)\)-optimal |
| 54150.e2 | 54150m2 | \([1, 1, 0, -19140, 1011150]\) | \(131872229/18\) | \(105853232250\) | \([2]\) | \(115200\) | \(1.1335\) | |
| 54150.e3 | 54150m3 | \([1, 1, 0, -10115, -1885875]\) | \(-19465109/248832\) | \(-1463315082624000\) | \([2]\) | \(288000\) | \(1.5917\) | |
| 54150.e1 | 54150m4 | \([1, 1, 0, -298915, -62822675]\) | \(502270291349/1889568\) | \(11112048908676000\) | \([2]\) | \(576000\) | \(1.9382\) |
Rank
sage: E.rank()
The elliptic curves in class 54150m have rank \(1\).
Complex multiplication
The elliptic curves in class 54150m do not have complex multiplication.Modular form 54150.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
