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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 493680br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
493680.br4 | 493680br1 | \([0, -1, 0, -36258416, 84047206080]\) | \(726497538898787209/1038579300\) | \(7536257365144780800\) | \([2]\) | \(33177600\) | \(2.8935\) | \(\Gamma_0(N)\)-optimal |
493680.br3 | 493680br2 | \([0, -1, 0, -36587536, 82443996736]\) | \(746461053445307689/27443694341250\) | \(199140059508241167360000\) | \([2]\) | \(66355200\) | \(3.2401\) | |
493680.br2 | 493680br3 | \([0, -1, 0, -46161056, 34550105856]\) | \(1499114720492202169/796539777000000\) | \(5779942620700250112000000\) | \([2]\) | \(99532800\) | \(3.4428\) | |
493680.br1 | 493680br4 | \([0, -1, 0, -426623776, -3365569130240]\) | \(1183430669265454849849/10449720703125000\) | \(75826453129416000000000000\) | \([2]\) | \(199065600\) | \(3.7894\) |
Rank
sage: E.rank()
The elliptic curves in class 493680br have rank \(0\).
Complex multiplication
The elliptic curves in class 493680br do not have complex multiplication.Modular form 493680.2.a.br
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.