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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 13552.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13552.k1 | 13552e3 | \([0, 0, 0, -30371, 2009810]\) | \(1707831108/26411\) | \(47911626312704\) | \([4]\) | \(30720\) | \(1.4263\) | |
| 13552.k2 | 13552e2 | \([0, 0, 0, -3751, -39930]\) | \(12869712/5929\) | \(2688917803264\) | \([2, 2]\) | \(15360\) | \(1.0798\) | |
| 13552.k3 | 13552e1 | \([0, 0, 0, -3146, -67881]\) | \(121485312/77\) | \(2182563152\) | \([2]\) | \(7680\) | \(0.73318\) | \(\Gamma_0(N)\)-optimal |
| 13552.k4 | 13552e4 | \([0, 0, 0, 13189, -300806]\) | \(139863132/102487\) | \(-185919459539968\) | \([2]\) | \(30720\) | \(1.4263\) |
Rank
sage: E.rank()
The elliptic curves in class 13552.k have rank \(1\).
Complex multiplication
The elliptic curves in class 13552.k do not have complex multiplication.Modular form 13552.2.a.k
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.
