Show commands:
SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 115520ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
115520.cv1 | 115520ba1 | \([0, -1, 0, -1330405, -550412475]\) | \(5405726654464/407253125\) | \(19619412024963200000\) | \([2]\) | \(2764800\) | \(2.4472\) | \(\Gamma_0(N)\)-optimal |
115520.cv2 | 115520ba2 | \([0, -1, 0, 1276015, -2446322383]\) | \(298091207216/3525390625\) | \(-2717370086560000000000\) | \([2]\) | \(5529600\) | \(2.7937\) |
Rank
sage: E.rank()
The elliptic curves in class 115520ba have rank \(1\).
Complex multiplication
The elliptic curves in class 115520ba do not have complex multiplication.Modular form 115520.2.a.ba
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.