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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 40768.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40768.ba1 | 40768dr3 | \([0, -1, 0, -1441057, -665360191]\) | \(-10730978619193/6656\) | \(-205277559259136\) | \([]\) | \(435456\) | \(2.0671\) | |
| 40768.ba2 | 40768dr2 | \([0, -1, 0, -14177, -1290239]\) | \(-10218313/17576\) | \(-542061054918656\) | \([]\) | \(145152\) | \(1.5178\) | |
| 40768.ba3 | 40768dr1 | \([0, -1, 0, 1503, 36289]\) | \(12167/26\) | \(-801865465856\) | \([]\) | \(48384\) | \(0.96845\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 40768.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 40768.ba do not have complex multiplication.Modular form 40768.2.a.ba
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.
