Show commands:
SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 407330.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
407330.q1 | 407330q2 | \([1, 0, 0, -18210836, 20121170416]\) | \(4511763717106237201/1429324759940000\) | \(211591361507429486660000\) | \([2]\) | \(74342400\) | \(3.1797\) | \(\Gamma_0(N)\)-optimal* |
407330.q2 | 407330q1 | \([1, 0, 0, 3203084, 2137760400]\) | \(24550575200187119/27540461132800\) | \(-4076976647263995059200\) | \([2]\) | \(37171200\) | \(2.8331\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 407330.q have rank \(1\).
Complex multiplication
The elliptic curves in class 407330.q do not have complex multiplication.Modular form 407330.2.a.q
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.