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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 10816bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10816.z3 | 10816bf1 | \([0, 1, 0, 5183, -233921]\) | \(12167/26\) | \(-32898294480896\) | \([]\) | \(21504\) | \(1.2780\) | \(\Gamma_0(N)\)-optimal |
| 10816.z2 | 10816bf2 | \([0, 1, 0, -48897, 8278271]\) | \(-10218313/17576\) | \(-22239247069085696\) | \([]\) | \(64512\) | \(1.8273\) | |
| 10816.z1 | 10816bf3 | \([0, 1, 0, -4970177, 4263216959]\) | \(-10730978619193/6656\) | \(-8421963387109376\) | \([]\) | \(193536\) | \(2.3766\) |
Rank
sage: E.rank()
The elliptic curves in class 10816bf have rank \(2\).
Complex multiplication
The elliptic curves in class 10816bf do not have complex multiplication.Modular form 10816.2.a.bf
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
