Show commands:
SageMath
E = EllipticCurve("nh1")
E.isogeny_class()
Elliptic curves in class 418950.nh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
418950.nh1 | 418950nh2 | \([1, -1, 1, -330980, -72053103]\) | \(2992209121/54150\) | \(72566178939843750\) | \([2]\) | \(6635520\) | \(2.0306\) | \(\Gamma_0(N)\)-optimal* |
418950.nh2 | 418950nh1 | \([1, -1, 1, -230, -3257103]\) | \(-1/3420\) | \(-4583127090937500\) | \([2]\) | \(3317760\) | \(1.6840\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 418950.nh have rank \(0\).
Complex multiplication
The elliptic curves in class 418950.nh do not have complex multiplication.Modular form 418950.2.a.nh
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.