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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 40656k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40656.be4 | 40656k1 | \([0, -1, 0, 3348, -2952288]\) | \(9148592/8301447\) | \(-3764869055684352\) | \([2]\) | \(245760\) | \(1.6677\) | \(\Gamma_0(N)\)-optimal |
| 40656.be3 | 40656k2 | \([0, -1, 0, -289472, -58470960]\) | \(1478729816932/38900169\) | \(70567958828860416\) | \([2, 2]\) | \(491520\) | \(2.0143\) | |
| 40656.be2 | 40656k3 | \([0, -1, 0, -662152, 123396880]\) | \(8849350367426/3314597517\) | \(12025879944835147776\) | \([2]\) | \(983040\) | \(2.3609\) | |
| 40656.be1 | 40656k4 | \([0, -1, 0, -4601912, -3798218928]\) | \(2970658109581346/2139291\) | \(7761683462658048\) | \([2]\) | \(983040\) | \(2.3609\) |
Rank
sage: E.rank()
The elliptic curves in class 40656k have rank \(0\).
Complex multiplication
The elliptic curves in class 40656k do not have complex multiplication.Modular form 40656.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
