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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 2400k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2400.bg3 | 2400k1 | \([0, 1, 0, -758, 7488]\) | \(48228544/2025\) | \(2025000000\) | \([2, 2]\) | \(1536\) | \(0.55046\) | \(\Gamma_0(N)\)-optimal |
| 2400.bg2 | 2400k2 | \([0, 1, 0, -2008, -25012]\) | \(111980168/32805\) | \(262440000000\) | \([2]\) | \(3072\) | \(0.89704\) | |
| 2400.bg1 | 2400k3 | \([0, 1, 0, -12008, 502488]\) | \(23937672968/45\) | \(360000000\) | \([2]\) | \(3072\) | \(0.89704\) | |
| 2400.bg4 | 2400k4 | \([0, 1, 0, 367, 28863]\) | \(85184/5625\) | \(-360000000000\) | \([2]\) | \(3072\) | \(0.89704\) |
Rank
sage: E.rank()
The elliptic curves in class 2400k have rank \(0\).
Complex multiplication
The elliptic curves in class 2400k do not have complex multiplication.Modular form 2400.2.a.k
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.
