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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 138720.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 138720.b1 | 138720w4 | \([0, -1, 0, -138816, -19860840]\) | \(23937672968/45\) | \(556129589760\) | \([2]\) | \(589824\) | \(1.5089\) | |
| 138720.b2 | 138720w2 | \([0, -1, 0, -23216, 964500]\) | \(111980168/32805\) | \(405418470935040\) | \([2]\) | \(589824\) | \(1.5089\) | |
| 138720.b3 | 138720w1 | \([0, -1, 0, -8766, -301320]\) | \(48228544/2025\) | \(3128228942400\) | \([2, 2]\) | \(294912\) | \(1.1624\) | \(\Gamma_0(N)\)-optimal |
| 138720.b4 | 138720w3 | \([0, -1, 0, 4239, -1131039]\) | \(85184/5625\) | \(-556129589760000\) | \([2]\) | \(589824\) | \(1.5089\) |
Rank
sage: E.rank()
The elliptic curves in class 138720.b have rank \(2\).
Complex multiplication
The elliptic curves in class 138720.b do not have complex multiplication.Modular form 138720.2.a.b
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
