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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 480h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 480.h3 | 480h1 | \([0, 1, 0, -30, -72]\) | \(48228544/2025\) | \(129600\) | \([2, 2]\) | \(64\) | \(-0.25425\) | \(\Gamma_0(N)\)-optimal |
| 480.h1 | 480h2 | \([0, 1, 0, -480, -4212]\) | \(23937672968/45\) | \(23040\) | \([2]\) | \(128\) | \(0.092319\) | |
| 480.h2 | 480h3 | \([0, 1, 0, -80, 168]\) | \(111980168/32805\) | \(16796160\) | \([4]\) | \(128\) | \(0.092319\) | |
| 480.h4 | 480h4 | \([0, 1, 0, 15, -225]\) | \(85184/5625\) | \(-23040000\) | \([4]\) | \(128\) | \(0.092319\) |
Rank
sage: E.rank()
The elliptic curves in class 480h have rank \(0\).
Complex multiplication
The elliptic curves in class 480h do not have complex multiplication.Modular form 480.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
