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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 79968bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
79968.bu3 | 79968bd1 | \([0, 1, 0, -4034, -87984]\) | \(964430272/127449\) | \(959631833664\) | \([2, 2]\) | \(86016\) | \(1.0271\) | \(\Gamma_0(N)\)-optimal |
79968.bu4 | 79968bd2 | \([0, 1, 0, 6256, -454308]\) | \(449455096/1753941\) | \(-105650895211008\) | \([2]\) | \(172032\) | \(1.3737\) | |
79968.bu2 | 79968bd3 | \([0, 1, 0, -16529, 724191]\) | \(1036433728/122451\) | \(59007949615104\) | \([2]\) | \(172032\) | \(1.3737\) | |
79968.bu1 | 79968bd4 | \([0, 1, 0, -62344, -6012280]\) | \(444893916104/9639\) | \(580617580032\) | \([2]\) | \(172032\) | \(1.3737\) |
Rank
sage: E.rank()
The elliptic curves in class 79968bd have rank \(0\).
Complex multiplication
The elliptic curves in class 79968bd do not have complex multiplication.Modular form 79968.2.a.bd
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.