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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 51984.br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
51984.br1 | 51984cl3 | \([0, 0, 0, -22250235, 40396752682]\) | \(8671983378625/82308\) | \(11562483630779154432\) | \([2]\) | \(2488320\) | \(2.8202\) | |
51984.br2 | 51984cl4 | \([0, 0, 0, -21730395, 42374120074]\) | \(-8078253774625/846825858\) | \(-118960612835271330373632\) | \([2]\) | \(4976640\) | \(3.1667\) | |
51984.br3 | 51984cl1 | \([0, 0, 0, -416955, -7915286]\) | \(57066625/32832\) | \(4612181836100272128\) | \([2]\) | \(829440\) | \(2.2709\) | \(\Gamma_0(N)\)-optimal |
51984.br4 | 51984cl2 | \([0, 0, 0, 1662405, -63226262]\) | \(3616805375/2105352\) | \(-295756160239929950208\) | \([2]\) | \(1658880\) | \(2.6174\) |
Rank
sage: E.rank()
The elliptic curves in class 51984.br have rank \(0\).
Complex multiplication
The elliptic curves in class 51984.br do not have complex multiplication.Modular form 51984.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.