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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 195195.br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
195195.br1 | 195195bw3 | \([1, 1, 0, -148892, 22051359]\) | \(75627935783569/396165\) | \(1912212787485\) | \([2]\) | \(884736\) | \(1.5526\) | |
195195.br2 | 195195bw2 | \([1, 1, 0, -9467, 328944]\) | \(19443408769/1334025\) | \(6439083876225\) | \([2, 2]\) | \(442368\) | \(1.2060\) | |
195195.br3 | 195195bw1 | \([1, 1, 0, -1862, -25449]\) | \(148035889/31185\) | \(150524038665\) | \([2]\) | \(221184\) | \(0.85947\) | \(\Gamma_0(N)\)-optimal |
195195.br4 | 195195bw4 | \([1, 1, 0, 8278, 1439781]\) | \(12994449551/192163125\) | \(-927534701218125\) | \([2]\) | \(884736\) | \(1.5526\) |
Rank
sage: E.rank()
The elliptic curves in class 195195.br have rank \(0\).
Complex multiplication
The elliptic curves in class 195195.br do not have complex multiplication.Modular form 195195.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.