Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 457776.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
457776.d1 | 457776d2 | \([0, 0, 0, -55616420907, -5048387278793190]\) | \(9776604686860471347243/147962546281\) | \(287936396490710924854013952\) | \([2]\) | \(1061683200\) | \(4.6266\) | |
457776.d2 | 457776d1 | \([0, 0, 0, -3479271867, -78726369449430]\) | \(2393558463315519963/9284733153971\) | \(18068171127949411836763410432\) | \([2]\) | \(530841600\) | \(4.2800\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 457776.d have rank \(0\).
Complex multiplication
The elliptic curves in class 457776.d do not have complex multiplication.Modular form 457776.2.a.d
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.