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SageMath
E = EllipticCurve("fq1")
E.isogeny_class()
Elliptic curves in class 46800fq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46800.o2 | 46800fq1 | \([0, 0, 0, -1281315, -558249950]\) | \(623295446073461/5458752\) | \(2037468266496000\) | \([2]\) | \(589824\) | \(2.1044\) | \(\Gamma_0(N)\)-optimal |
| 46800.o1 | 46800fq2 | \([0, 0, 0, -1310115, -531840350]\) | \(666276475992821/58199166792\) | \(21722722606780416000\) | \([2]\) | \(1179648\) | \(2.4510\) |
Rank
sage: E.rank()
The elliptic curves in class 46800fq have rank \(1\).
Complex multiplication
The elliptic curves in class 46800fq do not have complex multiplication.Modular form 46800.2.a.fq
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.
