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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 1344d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1344.f4 | 1344d1 | \([0, -1, 0, 27, -27]\) | \(2048000/1323\) | \(-1354752\) | \([2]\) | \(192\) | \(-0.13450\) | \(\Gamma_0(N)\)-optimal |
| 1344.f3 | 1344d2 | \([0, -1, 0, -113, -111]\) | \(9826000/5103\) | \(83607552\) | \([2]\) | \(384\) | \(0.21208\) | |
| 1344.f2 | 1344d3 | \([0, -1, 0, -453, -3675]\) | \(-10061824000/352947\) | \(-361417728\) | \([2]\) | \(576\) | \(0.41481\) | |
| 1344.f1 | 1344d4 | \([0, -1, 0, -7313, -238287]\) | \(2640279346000/3087\) | \(50577408\) | \([2]\) | \(1152\) | \(0.76138\) |
Rank
sage: E.rank()
The elliptic curves in class 1344d have rank \(0\).
Complex multiplication
The elliptic curves in class 1344d do not have complex multiplication.Modular form 1344.2.a.d
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
