Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 1850.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1850.j1 | 1850o2 | \([1, -1, 1, -341430, -76703803]\) | \(2253707317528029/700928\) | \(1369000000000\) | \([2]\) | \(8640\) | \(1.6910\) | |
1850.j2 | 1850o1 | \([1, -1, 1, -21430, -1183803]\) | \(557238592989/9699328\) | \(18944000000000\) | \([2]\) | \(4320\) | \(1.3445\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1850.j have rank \(1\).
Complex multiplication
The elliptic curves in class 1850.j do not have complex multiplication.Modular form 1850.2.a.j
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.