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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 15600.cu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15600.cu1 | 15600cc4 | \([0, 1, 0, -478408, 120723188]\) | \(189208196468929/10860320250\) | \(695060496000000000\) | \([2]\) | \(165888\) | \(2.1777\) | |
| 15600.cu2 | 15600cc2 | \([0, 1, 0, -82408, -9092812]\) | \(967068262369/4928040\) | \(315394560000000\) | \([2]\) | \(55296\) | \(1.6284\) | |
| 15600.cu3 | 15600cc1 | \([0, 1, 0, -2408, -292812]\) | \(-24137569/561600\) | \(-35942400000000\) | \([2]\) | \(27648\) | \(1.2818\) | \(\Gamma_0(N)\)-optimal |
| 15600.cu4 | 15600cc3 | \([0, 1, 0, 21592, 7723188]\) | \(17394111071/411937500\) | \(-26364000000000000\) | \([2]\) | \(82944\) | \(1.8311\) |
Rank
sage: E.rank()
The elliptic curves in class 15600.cu have rank \(1\).
Complex multiplication
The elliptic curves in class 15600.cu do not have complex multiplication.Modular form 15600.2.a.cu
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
