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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 52800.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
52800.d1 | 52800v4 | \([0, -1, 0, -234433, 43724737]\) | \(347873904937/395307\) | \(1619177472000000\) | \([2]\) | \(393216\) | \(1.8318\) | |
52800.d2 | 52800v2 | \([0, -1, 0, -18433, 308737]\) | \(169112377/88209\) | \(361304064000000\) | \([2, 2]\) | \(196608\) | \(1.4852\) | |
52800.d3 | 52800v1 | \([0, -1, 0, -10433, -403263]\) | \(30664297/297\) | \(1216512000000\) | \([2]\) | \(98304\) | \(1.1387\) | \(\Gamma_0(N)\)-optimal |
52800.d4 | 52800v3 | \([0, -1, 0, 69567, 2332737]\) | \(9090072503/5845851\) | \(-23944605696000000\) | \([2]\) | \(393216\) | \(1.8318\) |
Rank
sage: E.rank()
The elliptic curves in class 52800.d have rank \(1\).
Complex multiplication
The elliptic curves in class 52800.d do not have complex multiplication.Modular form 52800.2.a.d
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.