Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 190440.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
190440.k1 | 190440bu2 | \([0, 0, 0, -585603, -171481698]\) | \(3721734/25\) | \(149186068643174400\) | \([2]\) | \(2162688\) | \(2.1300\) | |
190440.k2 | 190440bu1 | \([0, 0, 0, -14283, -5913162]\) | \(-108/5\) | \(-14918606864317440\) | \([2]\) | \(1081344\) | \(1.7835\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 190440.k have rank \(0\).
Complex multiplication
The elliptic curves in class 190440.k do not have complex multiplication.Modular form 190440.2.a.k
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.