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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 84966bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
84966.ca2 | 84966bs1 | \([1, 0, 1, -3618431, -2648601070]\) | \(1845026709625/793152\) | \(2252362001887835712\) | \([2]\) | \(2488320\) | \(2.4817\) | \(\Gamma_0(N)\)-optimal |
84966.ca3 | 84966bs2 | \([1, 0, 1, -3051991, -3505738078]\) | \(-1107111813625/1228691592\) | \(-3489190286174493497352\) | \([2]\) | \(4976640\) | \(2.8283\) | |
84966.ca1 | 84966bs3 | \([1, 0, 1, -10628126, 10081769744]\) | \(46753267515625/11591221248\) | \(32916296364971780210688\) | \([2]\) | \(7464960\) | \(3.0310\) | |
84966.ca4 | 84966bs4 | \([1, 0, 1, 25624034, 63937978640]\) | \(655215969476375/1001033261568\) | \(-2842695071035072667140608\) | \([2]\) | \(14929920\) | \(3.3776\) |
Rank
sage: E.rank()
The elliptic curves in class 84966bs have rank \(1\).
Complex multiplication
The elliptic curves in class 84966bs do not have complex multiplication.Modular form 84966.2.a.bs
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.