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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 87856.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 87856.n1 | 87856g3 | \([0, 1, 0, -395448, 769793876]\) | \(-69173457625/2550136832\) | \(-252125608926582407168\) | \([]\) | \(2177280\) | \(2.5949\) | |
| 87856.n2 | 87856g1 | \([0, 1, 0, -71768, -7426540]\) | \(-413493625/152\) | \(-15027857358848\) | \([]\) | \(241920\) | \(1.4963\) | \(\Gamma_0(N)\)-optimal |
| 87856.n3 | 87856g2 | \([0, 1, 0, 43832, -28114316]\) | \(94196375/3511808\) | \(-347203616418824192\) | \([]\) | \(725760\) | \(2.0456\) |
Rank
sage: E.rank()
The elliptic curves in class 87856.n have rank \(0\).
Complex multiplication
The elliptic curves in class 87856.n do not have complex multiplication.Modular form 87856.2.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.
