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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 163254.bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
163254.bs1 | 163254ck4 | \([1, 0, 1, -30225485, -63962454814]\) | \(632678989847546725777/80515134\) | \(388631173427406\) | \([2]\) | \(8847360\) | \(2.6595\) | |
163254.bs2 | 163254ck3 | \([1, 0, 1, -2161345, -692760742]\) | \(231331938231569617/90942310746882\) | \(438961163993846759538\) | \([2]\) | \(8847360\) | \(2.6595\) | |
163254.bs3 | 163254ck2 | \([1, 0, 1, -1889255, -999351754]\) | \(154502321244119857/55101928644\) | \(265966485096216996\) | \([2, 2]\) | \(4423680\) | \(2.3129\) | |
163254.bs4 | 163254ck1 | \([1, 0, 1, -101235, -20232002]\) | \(-23771111713777/22848457968\) | \(-110285142556064112\) | \([2]\) | \(2211840\) | \(1.9663\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 163254.bs have rank \(0\).
Complex multiplication
The elliptic curves in class 163254.bs do not have complex multiplication.Modular form 163254.2.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 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.