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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 32760.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32760.l1 | 32760bh4 | \([0, 0, 0, -625323, 190326022]\) | \(18112543427820242/316031625\) | \(471832687872000\) | \([2]\) | \(294912\) | \(1.9440\) | |
32760.l2 | 32760bh2 | \([0, 0, 0, -40323, 2775022]\) | \(9713030100484/1164515625\) | \(869306256000000\) | \([2, 2]\) | \(147456\) | \(1.5974\) | |
32760.l3 | 32760bh1 | \([0, 0, 0, -9903, -333902]\) | \(575514878416/74972625\) | \(13991691168000\) | \([2]\) | \(73728\) | \(1.2508\) | \(\Gamma_0(N)\)-optimal |
32760.l4 | 32760bh3 | \([0, 0, 0, 57957, 14195158]\) | \(14420619677518/66650390625\) | \(-99508500000000000\) | \([2]\) | \(294912\) | \(1.9440\) |
Rank
sage: E.rank()
The elliptic curves in class 32760.l have rank \(0\).
Complex multiplication
The elliptic curves in class 32760.l do not have complex multiplication.Modular form 32760.2.a.l
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.