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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 2880.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2880.u1 | 2880x4 | \([0, 0, 0, -13932, 165456]\) | \(57960603/31250\) | \(161243136000000\) | \([2]\) | \(9216\) | \(1.4172\) | |
| 2880.u2 | 2880x2 | \([0, 0, 0, -8172, -284336]\) | \(8527173507/200\) | \(1415577600\) | \([2]\) | \(3072\) | \(0.86793\) | |
| 2880.u3 | 2880x1 | \([0, 0, 0, -492, -4784]\) | \(-1860867/320\) | \(-2264924160\) | \([2]\) | \(1536\) | \(0.52136\) | \(\Gamma_0(N)\)-optimal |
| 2880.u4 | 2880x3 | \([0, 0, 0, 3348, 20304]\) | \(804357/500\) | \(-2579890176000\) | \([2]\) | \(4608\) | \(1.0707\) |
Rank
sage: E.rank()
The elliptic curves in class 2880.u have rank \(1\).
Complex multiplication
The elliptic curves in class 2880.u do not have complex multiplication.Modular form 2880.2.a.u
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
