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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 141120.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.x1 | 141120lg3 | \([0, 0, 0, -1200108, 505779568]\) | \(68017239368/39375\) | \(110658879959040000\) | \([2]\) | \(1572864\) | \(2.2160\) | |
| 141120.x2 | 141120lg4 | \([0, 0, 0, -706188, -225123248]\) | \(13858588808/229635\) | \(645362587921121280\) | \([2]\) | \(1572864\) | \(2.2160\) | |
| 141120.x3 | 141120lg2 | \([0, 0, 0, -88788, 4796512]\) | \(220348864/99225\) | \(34857547187097600\) | \([2, 2]\) | \(786432\) | \(1.8695\) | |
| 141120.x4 | 141120lg1 | \([0, 0, 0, 19257, 561148]\) | \(143877824/108045\) | \(-593062434780480\) | \([2]\) | \(393216\) | \(1.5229\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141120.x have rank \(1\).
Complex multiplication
The elliptic curves in class 141120.x do not have complex multiplication.Modular form 141120.2.a.x
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.
