Show commands:
SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 1290.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1290.m1 | 1290m1 | \([1, 0, 0, -191, 921]\) | \(770842973809/66873600\) | \(66873600\) | \([2]\) | \(640\) | \(0.24229\) | \(\Gamma_0(N)\)-optimal |
1290.m2 | 1290m2 | \([1, 0, 0, 209, 4361]\) | \(1009328859791/8734528080\) | \(-8734528080\) | \([2]\) | \(1280\) | \(0.58887\) |
Rank
sage: E.rank()
The elliptic curves in class 1290.m have rank \(1\).
Complex multiplication
The elliptic curves in class 1290.m do not have complex multiplication.Modular form 1290.2.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.