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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 18816j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18816.w2 | 18816j1 | \([0, -1, 0, 82, -510]\) | \(4000/9\) | \(-135531648\) | \([2]\) | \(5760\) | \(0.24451\) | \(\Gamma_0(N)\)-optimal |
| 18816.w1 | 18816j2 | \([0, -1, 0, -653, -5067]\) | \(16000/3\) | \(5782683648\) | \([2]\) | \(11520\) | \(0.59108\) |
Rank
sage: E.rank()
The elliptic curves in class 18816j have rank \(0\).
Complex multiplication
The elliptic curves in class 18816j do not have complex multiplication.Modular form 18816.2.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.
