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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 327600.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 327600.x1 | 327600x3 | \([0, 0, 0, -7043475, 7193511250]\) | \(828279937799497/193444524\) | \(9025347711744000000\) | \([2]\) | \(9437184\) | \(2.6278\) | |
| 327600.x2 | 327600x2 | \([0, 0, 0, -491475, 84591250]\) | \(281397674377/96589584\) | \(4506483631104000000\) | \([2, 2]\) | \(4718592\) | \(2.2812\) | |
| 327600.x3 | 327600x1 | \([0, 0, 0, -203475, -34352750]\) | \(19968681097/628992\) | \(29346250752000000\) | \([2]\) | \(2359296\) | \(1.9347\) | \(\Gamma_0(N)\)-optimal |
| 327600.x4 | 327600x4 | \([0, 0, 0, 1452525, 588087250]\) | \(7264187703863/7406095788\) | \(-345538805084928000000\) | \([2]\) | \(9437184\) | \(2.6278\) |
Rank
sage: E.rank()
The elliptic curves in class 327600.x have rank \(1\).
Complex multiplication
The elliptic curves in class 327600.x do not have complex multiplication.Modular form 327600.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
