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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 50820m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
50820.m3 | 50820m1 | \([0, 1, 0, -322021, -71484976]\) | \(-130287139815424/2250652635\) | \(-63794694923411760\) | \([2]\) | \(622080\) | \(2.0225\) | \(\Gamma_0(N)\)-optimal |
50820.m2 | 50820m2 | \([0, 1, 0, -5173516, -4530979180]\) | \(33766427105425744/9823275\) | \(4455047905862400\) | \([2]\) | \(1244160\) | \(2.3691\) | |
50820.m4 | 50820m3 | \([0, 1, 0, 1246139, -341639740]\) | \(7549996227362816/6152409907875\) | \(-174389911180879086000\) | \([2]\) | \(1866240\) | \(2.5718\) | |
50820.m1 | 50820m4 | \([0, 1, 0, -6001156, -2985452956]\) | \(52702650535889104/22020583921875\) | \(9986766764344524000000\) | \([2]\) | \(3732480\) | \(2.9184\) |
Rank
sage: E.rank()
The elliptic curves in class 50820m have rank \(0\).
Complex multiplication
The elliptic curves in class 50820m do not have complex multiplication.Modular form 50820.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.