Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 443760.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
443760.f1 | 443760f1 | \([0, -1, 0, -4571542176, -118669594477824]\) | \(408076159454905367161/1190206406250000\) | \(30817184961133906560000000000\) | \([2]\) | \(468357120\) | \(4.3370\) | \(\Gamma_0(N)\)-optimal |
443760.f2 | 443760f2 | \([0, -1, 0, -2722542176, -215546840077824]\) | \(-86193969101536367161/725294740213012500\) | \(-18779551213226359220122060800000\) | \([2]\) | \(936714240\) | \(4.6835\) |
Rank
sage: E.rank()
The elliptic curves in class 443760.f have rank \(1\).
Complex multiplication
The elliptic curves in class 443760.f do not have complex multiplication.Modular form 443760.2.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.