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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 40768bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40768.cn3 | 40768bl1 | \([0, 1, 0, 1503, -36289]\) | \(12167/26\) | \(-801865465856\) | \([]\) | \(48384\) | \(0.96845\) | \(\Gamma_0(N)\)-optimal |
| 40768.cn2 | 40768bl2 | \([0, 1, 0, -14177, 1290239]\) | \(-10218313/17576\) | \(-542061054918656\) | \([]\) | \(145152\) | \(1.5178\) | |
| 40768.cn1 | 40768bl3 | \([0, 1, 0, -1441057, 665360191]\) | \(-10730978619193/6656\) | \(-205277559259136\) | \([]\) | \(435456\) | \(2.0671\) |
Rank
sage: E.rank()
The elliptic curves in class 40768bl have rank \(1\).
Complex multiplication
The elliptic curves in class 40768bl do not have complex multiplication.Modular form 40768.2.a.bl
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.
