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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 59976.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59976.n1 | 59976bp4 | \([0, 0, 0, -240051, -41142850]\) | \(17418812548/1753941\) | \(154039005217649664\) | \([2]\) | \(491520\) | \(2.0341\) | |
| 59976.n2 | 59976bp2 | \([0, 0, 0, -54831, 4236050]\) | \(830321872/127449\) | \(2798286426964224\) | \([2, 2]\) | \(245760\) | \(1.6876\) | |
| 59976.n3 | 59976bp1 | \([0, 0, 0, -52626, 4646621]\) | \(11745974272/357\) | \(489896083152\) | \([4]\) | \(122880\) | \(1.3410\) | \(\Gamma_0(N)\)-optimal |
| 59976.n4 | 59976bp3 | \([0, 0, 0, 95109, 23338406]\) | \(1083360092/3306177\) | \(-290363368068523008\) | \([2]\) | \(491520\) | \(2.0341\) |
Rank
sage: E.rank()
The elliptic curves in class 59976.n have rank \(1\).
Complex multiplication
The elliptic curves in class 59976.n do not have complex multiplication.Modular form 59976.2.a.n
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.
