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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 43680.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 43680.l1 | 43680a4 | \([0, -1, 0, -16856, -836700]\) | \(1034529986960072/44983575\) | \(23031590400\) | \([2]\) | \(65536\) | \(1.0668\) | |
| 43680.l2 | 43680a3 | \([0, -1, 0, -5201, 135201]\) | \(3799337068864/319921875\) | \(1310400000000\) | \([2]\) | \(65536\) | \(1.0668\) | |
| 43680.l3 | 43680a1 | \([0, -1, 0, -1106, -11400]\) | \(2339923888576/419225625\) | \(26830440000\) | \([2, 2]\) | \(32768\) | \(0.72025\) | \(\Gamma_0(N)\)-optimal |
| 43680.l4 | 43680a2 | \([0, -1, 0, 2144, -68600]\) | \(2127774087928/5119712325\) | \(-2621292710400\) | \([2]\) | \(65536\) | \(1.0668\) |
Rank
sage: E.rank()
The elliptic curves in class 43680.l have rank \(0\).
Complex multiplication
The elliptic curves in class 43680.l do not have complex multiplication.Modular form 43680.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
