Show commands:
SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 63882.cj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 63882.cj1 | 63882bq3 | \([1, -1, 1, -179510, 29318735]\) | \(-545407363875/14\) | \(-16420804218\) | \([]\) | \(221616\) | \(1.4764\) | |
| 63882.cj2 | 63882bq1 | \([1, -1, 1, -2060, 46583]\) | \(-7414875/2744\) | \(-357608625192\) | \([]\) | \(73872\) | \(0.92705\) | \(\Gamma_0(N)\)-optimal |
| 63882.cj3 | 63882bq2 | \([1, -1, 1, 15685, -469205]\) | \(4492125/3584\) | \(-340501796264448\) | \([]\) | \(221616\) | \(1.4764\) |
Rank
sage: E.rank()
The elliptic curves in class 63882.cj have rank \(0\).
Complex multiplication
The elliptic curves in class 63882.cj do not have complex multiplication.Modular form 63882.2.a.cj
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
