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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 10816.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10816.k1 | 10816i3 | \([0, -1, 0, -4970177, -4263216959]\) | \(-10730978619193/6656\) | \(-8421963387109376\) | \([]\) | \(193536\) | \(2.3766\) | |
| 10816.k2 | 10816i2 | \([0, -1, 0, -48897, -8278271]\) | \(-10218313/17576\) | \(-22239247069085696\) | \([]\) | \(64512\) | \(1.8273\) | |
| 10816.k3 | 10816i1 | \([0, -1, 0, 5183, 233921]\) | \(12167/26\) | \(-32898294480896\) | \([]\) | \(21504\) | \(1.2780\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10816.k have rank \(1\).
Complex multiplication
The elliptic curves in class 10816.k do not have complex multiplication.Modular form 10816.2.a.k
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
