Show commands:
SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 422370m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
422370.m2 | 422370m1 | \([1, -1, 0, -170640, -28512000]\) | \(-16022066761/998400\) | \(-34241572933401600\) | \([2]\) | \(4561920\) | \(1.9268\) | \(\Gamma_0(N)\)-optimal* |
422370.m1 | 422370m2 | \([1, -1, 0, -2769840, -1773614880]\) | \(68523370149961/243360\) | \(8346383402516640\) | \([2]\) | \(9123840\) | \(2.2734\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 422370m have rank \(0\).
Complex multiplication
The elliptic curves in class 422370m do not have complex multiplication.Modular form 422370.2.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 Cremona 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 Cremona labels.