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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 106560.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 106560.p1 | 106560en4 | \([0, 0, 0, -79788, -8355472]\) | \(2351575819592/98316585\) | \(2348573997957120\) | \([2]\) | \(589824\) | \(1.7143\) | |
| 106560.p2 | 106560en2 | \([0, 0, 0, -13188, 409088]\) | \(84951891136/24950025\) | \(74500375449600\) | \([2, 2]\) | \(294912\) | \(1.3677\) | |
| 106560.p3 | 106560en1 | \([0, 0, 0, -12063, 509888]\) | \(4160851280704/624375\) | \(29130840000\) | \([2]\) | \(147456\) | \(1.0211\) | \(\Gamma_0(N)\)-optimal |
| 106560.p4 | 106560en3 | \([0, 0, 0, 35412, 2722448]\) | \(205587930808/253011735\) | \(-6043911940177920\) | \([2]\) | \(589824\) | \(1.7143\) |
Rank
sage: E.rank()
The elliptic curves in class 106560.p have rank \(1\).
Complex multiplication
The elliptic curves in class 106560.p do not have complex multiplication.Modular form 106560.2.a.p
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
