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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 18240.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18240.m1 | 18240bs3 | \([0, -1, 0, -9761, -367935]\) | \(784767874322/35625\) | \(4669440000\) | \([2]\) | \(24576\) | \(0.93152\) | |
18240.m2 | 18240bs4 | \([0, -1, 0, -3041, 60801]\) | \(23735908082/1954815\) | \(256221511680\) | \([2]\) | \(24576\) | \(0.93152\) | |
18240.m3 | 18240bs2 | \([0, -1, 0, -641, -4959]\) | \(445138564/81225\) | \(5323161600\) | \([2, 2]\) | \(12288\) | \(0.58494\) | |
18240.m4 | 18240bs1 | \([0, -1, 0, 79, -495]\) | \(3286064/7695\) | \(-126074880\) | \([2]\) | \(6144\) | \(0.23837\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18240.m have rank \(0\).
Complex multiplication
The elliptic curves in class 18240.m do not have complex multiplication.Modular form 18240.2.a.m
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.