Show commands:
SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 22386m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22386.n3 | 22386m1 | \([1, 0, 1, -235, -1402]\) | \(1426487591593/179088\) | \(179088\) | \([2]\) | \(7808\) | \(0.030379\) | \(\Gamma_0(N)\)-optimal |
| 22386.n2 | 22386m2 | \([1, 0, 1, -255, -1154]\) | \(1823449422313/501132996\) | \(501132996\) | \([2, 2]\) | \(15616\) | \(0.37695\) | |
| 22386.n4 | 22386m3 | \([1, 0, 1, 655, -7342]\) | \(31145864569847/41657368662\) | \(-41657368662\) | \([2]\) | \(31232\) | \(0.72353\) | |
| 22386.n1 | 22386m4 | \([1, 0, 1, -1485, 20986]\) | \(361811696411593/16869440406\) | \(16869440406\) | \([2]\) | \(31232\) | \(0.72353\) |
Rank
sage: E.rank()
The elliptic curves in class 22386m have rank \(0\).
Complex multiplication
The elliptic curves in class 22386m do not have complex multiplication.Modular form 22386.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
