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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 13328o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13328.p4 | 13328o1 | \([0, 0, 0, -539, 2058]\) | \(35937/17\) | \(8192135168\) | \([2]\) | \(4608\) | \(0.59632\) | \(\Gamma_0(N)\)-optimal |
| 13328.p2 | 13328o2 | \([0, 0, 0, -4459, -113190]\) | \(20346417/289\) | \(139266297856\) | \([2, 2]\) | \(9216\) | \(0.94289\) | |
| 13328.p1 | 13328o3 | \([0, 0, 0, -71099, -7296982]\) | \(82483294977/17\) | \(8192135168\) | \([2]\) | \(18432\) | \(1.2895\) | |
| 13328.p3 | 13328o4 | \([0, 0, 0, -539, -305270]\) | \(-35937/83521\) | \(-40247960080384\) | \([2]\) | \(18432\) | \(1.2895\) |
Rank
sage: E.rank()
The elliptic curves in class 13328o have rank \(1\).
Complex multiplication
The elliptic curves in class 13328o do not have complex multiplication.Modular form 13328.2.a.o
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
