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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 73920.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
73920.u1 | 73920g4 | \([0, -1, 0, -17031201, 27058714785]\) | \(2084105208962185000201/31185000\) | \(8174960640000\) | \([2]\) | \(2359296\) | \(2.4812\) | |
73920.u2 | 73920g3 | \([0, -1, 0, -1154081, 347714721]\) | \(648474704552553481/176469171805080\) | \(46260334573670891520\) | \([2]\) | \(2359296\) | \(2.4812\) | |
73920.u3 | 73920g2 | \([0, -1, 0, -1064481, 423032481]\) | \(508859562767519881/62240270400\) | \(16315913443737600\) | \([2, 2]\) | \(1179648\) | \(2.1347\) | |
73920.u4 | 73920g1 | \([0, -1, 0, -60961, 7775905]\) | \(-95575628340361/43812679680\) | \(-11485231102033920\) | \([2]\) | \(589824\) | \(1.7881\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 73920.u have rank \(0\).
Complex multiplication
The elliptic curves in class 73920.u do not have complex multiplication.Modular form 73920.2.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.