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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 219024.br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
219024.br1 | 219024e3 | \([0, 0, 0, -2912715, -1913354118]\) | \(-189613868625/128\) | \(-1844835128967168\) | \([]\) | \(2322432\) | \(2.2450\) | |
219024.br2 | 219024e4 | \([0, 0, 0, -2304315, -2734961814]\) | \(-1159088625/2097152\) | \(-2448288078992844521472\) | \([]\) | \(6967296\) | \(2.7943\) | |
219024.br3 | 219024e2 | \([0, 0, 0, -114075, 15541578]\) | \(-140625/8\) | \(-9339477840396288\) | \([]\) | \(995328\) | \(1.8213\) | |
219024.br4 | 219024e1 | \([0, 0, 0, 7605, 39546]\) | \(3375/2\) | \(-28825548890112\) | \([]\) | \(331776\) | \(1.2720\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 219024.br have rank \(1\).
Complex multiplication
The elliptic curves in class 219024.br do not have complex multiplication.Modular form 219024.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 21 & 7 \\ 3 & 1 & 7 & 21 \\ 21 & 7 & 1 & 3 \\ 7 & 21 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.