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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 2736.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2736.n1 | 2736m3 | \([0, 0, 0, -12315, -4231222]\) | \(-69173457625/2550136832\) | \(-7614667778162688\) | \([]\) | \(12960\) | \(1.7276\) | |
| 2736.n2 | 2736m1 | \([0, 0, 0, -2235, 40682]\) | \(-413493625/152\) | \(-453869568\) | \([]\) | \(1440\) | \(0.62901\) | \(\Gamma_0(N)\)-optimal |
| 2736.n3 | 2736m2 | \([0, 0, 0, 1365, 154586]\) | \(94196375/3511808\) | \(-10486202499072\) | \([]\) | \(4320\) | \(1.1783\) |
Rank
sage: E.rank()
The elliptic curves in class 2736.n have rank \(1\).
Complex multiplication
The elliptic curves in class 2736.n do not have complex multiplication.Modular form 2736.2.a.n
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
