Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 430950j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
430950.j2 | 430950j1 | \([1, 1, 0, -3052650, -2081155500]\) | \(-41713327443241/639221760\) | \(-48209396002560000000\) | \([2]\) | \(18966528\) | \(2.5793\) | \(\Gamma_0(N)\)-optimal* |
430950.j1 | 430950j2 | \([1, 1, 0, -49020650, -132124627500]\) | \(172735174415217961/39657600\) | \(2990932196850000000\) | \([2]\) | \(37933056\) | \(2.9259\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 430950j have rank \(1\).
Complex multiplication
The elliptic curves in class 430950j do not have complex multiplication.Modular form 430950.2.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 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.