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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 4176.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4176.n1 | 4176bc2 | \([0, 0, 0, -65523, -6499406]\) | \(-10418796526321/82044596\) | \(-244983850942464\) | \([]\) | \(14400\) | \(1.5896\) | |
| 4176.n2 | 4176bc1 | \([0, 0, 0, 717, 12274]\) | \(13651919/29696\) | \(-88671780864\) | \([]\) | \(2880\) | \(0.78490\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4176.n have rank \(0\).
Complex multiplication
The elliptic curves in class 4176.n do not have complex multiplication.Modular form 4176.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
