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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 2880.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2880.h1 | 2880v4 | \([0, 0, 0, -73548, 7677072]\) | \(8527173507/200\) | \(1031956070400\) | \([2]\) | \(9216\) | \(1.4172\) | |
| 2880.h2 | 2880v3 | \([0, 0, 0, -4428, 129168]\) | \(-1860867/320\) | \(-1651129712640\) | \([2]\) | \(4608\) | \(1.0707\) | |
| 2880.h3 | 2880v2 | \([0, 0, 0, -1548, -6128]\) | \(57960603/31250\) | \(221184000000\) | \([2]\) | \(3072\) | \(0.86793\) | |
| 2880.h4 | 2880v1 | \([0, 0, 0, 372, -752]\) | \(804357/500\) | \(-3538944000\) | \([2]\) | \(1536\) | \(0.52136\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2880.h have rank \(0\).
Complex multiplication
The elliptic curves in class 2880.h do not have complex multiplication.Modular form 2880.2.a.h
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
