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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 132600.cl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
132600.cl1 | 132600bx4 | \([0, 1, 0, -735808, -243180112]\) | \(2753580869496292/39328497\) | \(629255952000000\) | \([2]\) | \(1310720\) | \(1.9791\) | |
132600.cl2 | 132600bx2 | \([0, 1, 0, -47308, -3582112]\) | \(2927363579728/320445801\) | \(1281783204000000\) | \([2, 2]\) | \(655360\) | \(1.6325\) | |
132600.cl3 | 132600bx1 | \([0, 1, 0, -11183, 391638]\) | \(618724784128/87947613\) | \(21986903250000\) | \([2]\) | \(327680\) | \(1.2859\) | \(\Gamma_0(N)\)-optimal |
132600.cl4 | 132600bx3 | \([0, 1, 0, 63192, -17726112]\) | \(1744147297148/9513325341\) | \(-152213205456000000\) | \([2]\) | \(1310720\) | \(1.9791\) |
Rank
sage: E.rank()
The elliptic curves in class 132600.cl have rank \(0\).
Complex multiplication
The elliptic curves in class 132600.cl do not have complex multiplication.Modular form 132600.2.a.cl
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.