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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 2442.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2442.a1 | 2442c3 | \([1, 1, 0, -5607426, 5108517876]\) | \(19499096390516434897995817/15393430272\) | \(15393430272\) | \([4]\) | \(61440\) | \(2.1593\) | |
| 2442.a2 | 2442c2 | \([1, 1, 0, -350466, 79709940]\) | \(4760617885089919932457/133756441657344\) | \(133756441657344\) | \([2, 2]\) | \(30720\) | \(1.8127\) | |
| 2442.a3 | 2442c4 | \([1, 1, 0, -336386, 86426100]\) | \(-4209586785160189454377/801182513521564416\) | \(-801182513521564416\) | \([2]\) | \(61440\) | \(2.1593\) | |
| 2442.a4 | 2442c1 | \([1, 1, 0, -22786, 1132276]\) | \(1308451928740468777/194033737531392\) | \(194033737531392\) | \([2]\) | \(15360\) | \(1.4662\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2442.a have rank \(1\).
Complex multiplication
The elliptic curves in class 2442.a do not have complex multiplication.Modular form 2442.2.a.a
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.
