Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 302016j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 302016.j2 | 302016j1 | \([0, -1, 0, -127585, 14196481]\) | \(658275956099/132907008\) | \(46373071132557312\) | \([2]\) | \(4644864\) | \(1.9138\) | \(\Gamma_0(N)\)-optimal |
| 302016.j1 | 302016j2 | \([0, -1, 0, -1929825, 1032462081]\) | \(2278031600817539/131609088\) | \(45920209109778432\) | \([2]\) | \(9289728\) | \(2.2604\) |
Rank
sage: E.rank()
The elliptic curves in class 302016j have rank \(0\).
Complex multiplication
The elliptic curves in class 302016j do not have complex multiplication.Modular form 302016.2.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.
