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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 56350.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 56350.n1 | 56350b1 | \([1, -1, 0, -1650917, -269457259]\) | \(270701905514769/139540889600\) | \(256513220633600000000\) | \([2]\) | \(1769472\) | \(2.6083\) | \(\Gamma_0(N)\)-optimal |
| 56350.n2 | 56350b2 | \([1, -1, 0, 6189083, -2096177259]\) | \(14262456319278831/9284810958080\) | \(-17067948818861780000000\) | \([2]\) | \(3538944\) | \(2.9548\) |
Rank
sage: E.rank()
The elliptic curves in class 56350.n have rank \(0\).
Complex multiplication
The elliptic curves in class 56350.n do not have complex multiplication.Modular form 56350.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
