Show commands:
SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 493680.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
493680.m1 | 493680m2 | \([0, -1, 0, -270376, -1892240]\) | \(400951397082419/231720662400\) | \(1263289145976422400\) | \([2]\) | \(7741440\) | \(2.1629\) | \(\Gamma_0(N)\)-optimal* |
493680.m2 | 493680m1 | \([0, -1, 0, 67544, -270224]\) | \(6250857632461/3622256640\) | \(-19747731815792640\) | \([2]\) | \(3870720\) | \(1.8163\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 493680.m have rank \(0\).
Complex multiplication
The elliptic curves in class 493680.m do not have complex multiplication.Modular form 493680.2.a.m
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.