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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 54450l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54450.cp4 | 54450l1 | \([1, -1, 0, 17583, -248759]\) | \(804357/500\) | \(-373688648437500\) | \([2]\) | \(207360\) | \(1.4853\) | \(\Gamma_0(N)\)-optimal |
54450.cp3 | 54450l2 | \([1, -1, 0, -73167, -1973009]\) | \(57960603/31250\) | \(23355540527343750\) | \([2]\) | \(414720\) | \(1.8319\) | |
54450.cp2 | 54450l3 | \([1, -1, 0, -209292, 42025616]\) | \(-1860867/320\) | \(-174348175815000000\) | \([2]\) | \(622080\) | \(2.0346\) | |
54450.cp1 | 54450l4 | \([1, -1, 0, -3476292, 2495542616]\) | \(8527173507/200\) | \(108967609884375000\) | \([2]\) | \(1244160\) | \(2.3812\) |
Rank
sage: E.rank()
The elliptic curves in class 54450l have rank \(0\).
Complex multiplication
The elliptic curves in class 54450l do not have complex multiplication.Modular form 54450.2.a.l
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 Cremona 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 Cremona labels.