Show commands:
SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 466752n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
466752.n4 | 466752n1 | \([0, -1, 0, 39551, -2053247]\) | \(26100282937247/21962862207\) | \(-5757432550391808\) | \([2]\) | \(1966080\) | \(1.7118\) | \(\Gamma_0(N)\)-optimal* |
466752.n3 | 466752n2 | \([0, -1, 0, -193729, -17869631]\) | \(3067396672113073/1245074357241\) | \(326388772304584704\) | \([2, 2]\) | \(3932160\) | \(2.0583\) | \(\Gamma_0(N)\)-optimal* |
466752.n2 | 466752n3 | \([0, -1, 0, -1429249, 645604609]\) | \(1231708064988053953/26933399479701\) | \(7060429073206738944\) | \([2]\) | \(7864320\) | \(2.4049\) | \(\Gamma_0(N)\)-optimal* |
466752.n1 | 466752n4 | \([0, -1, 0, -2690689, -1697324927]\) | \(8218157522273610913/3262914972603\) | \(855353582578040832\) | \([2]\) | \(7864320\) | \(2.4049\) |
Rank
sage: E.rank()
The elliptic curves in class 466752n have rank \(0\).
Complex multiplication
The elliptic curves in class 466752n do not have complex multiplication.Modular form 466752.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.