Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 257600.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 257600.j1 | 257600j2 | \([0, 1, 0, -593, -3857]\) | \(11279504/3703\) | \(7583744000\) | \([2]\) | \(184320\) | \(0.59880\) | |
| 257600.j2 | 257600j1 | \([0, 1, 0, 107, -357]\) | \(1048576/1127\) | \(-144256000\) | \([2]\) | \(92160\) | \(0.25222\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 257600.j have rank \(1\).
Complex multiplication
The elliptic curves in class 257600.j do not have complex multiplication.Modular form 257600.2.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 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.
