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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 44400.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44400.v1 | 44400c4 | \([0, -1, 0, -133200008, -591659581488]\) | \(8167450100737631904002/124875\) | \(3996000000000\) | \([2]\) | \(2433024\) | \(2.8975\) | |
44400.v2 | 44400c3 | \([0, -1, 0, -8450008, -8950581488]\) | \(2085187657182084002/124500749500125\) | \(3984023984004000000000\) | \([2]\) | \(2433024\) | \(2.8975\) | |
44400.v3 | 44400c2 | \([0, -1, 0, -8325008, -9242581488]\) | \(3988023972023988004/15593765625\) | \(249500250000000000\) | \([2, 2]\) | \(1216512\) | \(2.5510\) | |
44400.v4 | 44400c1 | \([0, -1, 0, -512508, -148831488]\) | \(-3721915550952016/243896484375\) | \(-975585937500000000\) | \([2]\) | \(608256\) | \(2.2044\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 44400.v have rank \(1\).
Complex multiplication
The elliptic curves in class 44400.v do not have complex multiplication.Modular form 44400.2.a.v
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.