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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 254320y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 254320.y4 | 254320y1 | \([0, 0, 0, 3757, -68782]\) | \(59319/55\) | \(-5437711544320\) | \([2]\) | \(294912\) | \(1.1309\) | \(\Gamma_0(N)\)-optimal |
| 254320.y3 | 254320y2 | \([0, 0, 0, -19363, -619038]\) | \(8120601/3025\) | \(299074134937600\) | \([2, 2]\) | \(589824\) | \(1.4775\) | |
| 254320.y2 | 254320y3 | \([0, 0, 0, -134963, 18639922]\) | \(2749884201/73205\) | \(7237594065489920\) | \([2]\) | \(1179648\) | \(1.8241\) | |
| 254320.y1 | 254320y4 | \([0, 0, 0, -273683, -55094382]\) | \(22930509321/6875\) | \(679713943040000\) | \([2]\) | \(1179648\) | \(1.8241\) |
Rank
sage: E.rank()
The elliptic curves in class 254320y have rank \(0\).
Complex multiplication
The elliptic curves in class 254320y do not have complex multiplication.Modular form 254320.2.a.y
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.
