Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 448.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 448.f1 | 448d2 | \([0, -1, 0, -33, -31]\) | \(125000/49\) | \(1605632\) | \([2]\) | \(64\) | \(-0.11063\) | |
| 448.f2 | 448d1 | \([0, -1, 0, 7, -7]\) | \(8000/7\) | \(-28672\) | \([2]\) | \(32\) | \(-0.45720\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 448.f have rank \(0\).
Complex multiplication
The elliptic curves in class 448.f do not have complex multiplication.Modular form 448.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
