Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 249690.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 249690.f1 | 249690f3 | \([1, 1, 0, -583963, -119850257]\) | \(22023222535845979528249/6564806277121830150\) | \(6564806277121830150\) | \([2]\) | \(6619136\) | \(2.3162\) | |
| 249690.f2 | 249690f2 | \([1, 1, 0, -533213, -150066807]\) | \(16765911613813068220249/2620052663602500\) | \(2620052663602500\) | \([2, 2]\) | \(3309568\) | \(1.9696\) | |
| 249690.f3 | 249690f1 | \([1, 1, 0, -533193, -150078603]\) | \(16764025095699365996569/409491600\) | \(409491600\) | \([2]\) | \(1654784\) | \(1.6230\) | \(\Gamma_0(N)\)-optimal |
| 249690.f4 | 249690f4 | \([1, 1, 0, -482783, -179528013]\) | \(-12444602381446785105529/6690570482252343750\) | \(-6690570482252343750\) | \([2]\) | \(6619136\) | \(2.3162\) |
Rank
sage: E.rank()
The elliptic curves in class 249690.f have rank \(0\).
Complex multiplication
The elliptic curves in class 249690.f do not have complex multiplication.Modular form 249690.2.a.f
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.
