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SageMath
E = EllipticCurve("jd1")
E.isogeny_class()
Elliptic curves in class 100800jd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100800.hl1 | 100800jd1 | \([0, 0, 0, -73788300, 243438858000]\) | \(551105805571803/1376829440\) | \(111002148321361920000000\) | \([2]\) | \(15482880\) | \(3.2994\) | \(\Gamma_0(N)\)-optimal |
100800.hl2 | 100800jd2 | \([0, 0, 0, -46140300, 428072202000]\) | \(-134745327251163/903920796800\) | \(-72875511985825382400000000\) | \([2]\) | \(30965760\) | \(3.6459\) |
Rank
sage: E.rank()
The elliptic curves in class 100800jd have rank \(0\).
Complex multiplication
The elliptic curves in class 100800jd do not have complex multiplication.Modular form 100800.2.a.jd
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.