Show commands:
SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 430950.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 430950.m1 | 430950m1 | \([1, 1, 0, -1975275, -798001875]\) | \(11301253512121/2899962000\) | \(218711916894656250000\) | \([2]\) | \(18579456\) | \(2.6122\) | \(\Gamma_0(N)\)-optimal |
| 430950.m2 | 430950m2 | \([1, 1, 0, 4869225, -5103192375]\) | \(169286748026759/247257562500\) | \(-18647891062391601562500\) | \([2]\) | \(37158912\) | \(2.9588\) |
Rank
sage: E.rank()
The elliptic curves in class 430950.m have rank \(1\).
Complex multiplication
The elliptic curves in class 430950.m do not have complex multiplication.Modular form 430950.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
