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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 1785.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1785.l1 | 1785g3 | \([1, 1, 0, -297, 1806]\) | \(2912566550041/76531875\) | \(76531875\) | \([4]\) | \(512\) | \(0.29416\) | |
| 1785.l2 | 1785g2 | \([1, 1, 0, -42, -81]\) | \(8502154921/3186225\) | \(3186225\) | \([2, 2]\) | \(256\) | \(-0.052414\) | |
| 1785.l3 | 1785g1 | \([1, 1, 0, -37, -104]\) | \(5841725401/1785\) | \(1785\) | \([2]\) | \(128\) | \(-0.39899\) | \(\Gamma_0(N)\)-optimal |
| 1785.l4 | 1785g4 | \([1, 1, 0, 133, -396]\) | \(257138126279/236782035\) | \(-236782035\) | \([2]\) | \(512\) | \(0.29416\) |
Rank
sage: E.rank()
The elliptic curves in class 1785.l have rank \(0\).
Complex multiplication
The elliptic curves in class 1785.l do not have complex multiplication.Modular form 1785.2.a.l
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.
