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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 4928.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4928.n1 | 4928h3 | \([0, 0, 0, -330476, -73123664]\) | \(15226621995131793/2324168\) | \(609266696192\) | \([2]\) | \(18432\) | \(1.6669\) | |
4928.n2 | 4928h4 | \([0, 0, 0, -38636, 1122480]\) | \(24331017010833/12004097336\) | \(3146802092048384\) | \([4]\) | \(18432\) | \(1.6669\) | |
4928.n3 | 4928h2 | \([0, 0, 0, -20716, -1135440]\) | \(3750606459153/45914176\) | \(12036125753344\) | \([2, 2]\) | \(9216\) | \(1.3203\) | |
4928.n4 | 4928h1 | \([0, 0, 0, -236, -45904]\) | \(-5545233/3469312\) | \(-909459324928\) | \([2]\) | \(4608\) | \(0.97375\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4928.n have rank \(0\).
Complex multiplication
The elliptic curves in class 4928.n do not have complex multiplication.Modular form 4928.2.a.n
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.