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SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 482664cn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
482664.cn3 | 482664cn1 | \([0, 1, 0, -20167, 1095602]\) | \(11745974272/357\) | \(27570733008\) | \([2]\) | \(614400\) | \(1.1012\) | \(\Gamma_0(N)\)-optimal |
482664.cn2 | 482664cn2 | \([0, 1, 0, -21012, 997920]\) | \(830321872/127449\) | \(157484026941696\) | \([2, 2]\) | \(1228800\) | \(1.4478\) | |
482664.cn4 | 482664cn3 | \([0, 1, 0, 36448, 5548752]\) | \(1083360092/3306177\) | \(-16341283736773632\) | \([2]\) | \(2457600\) | \(1.7943\) | |
482664.cn1 | 482664cn4 | \([0, 1, 0, -91992, -9791040]\) | \(17418812548/1753941\) | \(8669120721171456\) | \([2]\) | \(2457600\) | \(1.7943\) |
Rank
sage: E.rank()
The elliptic curves in class 482664cn have rank \(0\).
Complex multiplication
The elliptic curves in class 482664cn do not have complex multiplication.Modular form 482664.2.a.cn
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.