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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 444360.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
444360.u1 | 444360u3 | \([0, -1, 0, -1976520, 1070203932]\) | \(5633270409316/14175\) | \(2148770536012800\) | \([2]\) | \(6307840\) | \(2.1802\) | \(\Gamma_0(N)\)-optimal* |
444360.u2 | 444360u4 | \([0, -1, 0, -347200, -57522500]\) | \(30534944836/8203125\) | \(1243501467600000000\) | \([2]\) | \(6307840\) | \(2.1802\) | |
444360.u3 | 444360u2 | \([0, -1, 0, -125020, 16330132]\) | \(5702413264/275625\) | \(10445412327840000\) | \([2, 2]\) | \(3153920\) | \(1.8336\) | \(\Gamma_0(N)\)-optimal* |
444360.u4 | 444360u1 | \([0, -1, 0, 4585, 984900]\) | \(4499456/180075\) | \(-426521003386800\) | \([2]\) | \(1576960\) | \(1.4871\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 444360.u have rank \(1\).
Complex multiplication
The elliptic curves in class 444360.u do not have complex multiplication.Modular form 444360.2.a.u
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.