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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 15162.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15162.r1 | 15162w3 | \([1, 1, 1, -6552699, -6458948385]\) | \(661397832743623417/443352042\) | \(20857887409039002\) | \([2]\) | \(460800\) | \(2.4475\) | |
| 15162.r2 | 15162w2 | \([1, 1, 1, -412089, -99732669]\) | \(164503536215257/4178071044\) | \(196561033145569764\) | \([2, 2]\) | \(230400\) | \(2.1009\) | |
| 15162.r3 | 15162w1 | \([1, 1, 1, -58309, 3146555]\) | \(466025146777/177366672\) | \(8344371344278032\) | \([4]\) | \(115200\) | \(1.7544\) | \(\Gamma_0(N)\)-optimal |
| 15162.r4 | 15162w4 | \([1, 1, 1, 68041, -317711689]\) | \(740480746823/927484650666\) | \(-43634332504559206746\) | \([2]\) | \(460800\) | \(2.4475\) |
Rank
sage: E.rank()
The elliptic curves in class 15162.r have rank \(0\).
Complex multiplication
The elliptic curves in class 15162.r do not have complex multiplication.Modular form 15162.2.a.r
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
