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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 1386.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1386.k1 | 1386l4 | \([1, -1, 1, -2039, 35925]\) | \(1285429208617/614922\) | \(448278138\) | \([2]\) | \(1024\) | \(0.61497\) | |
| 1386.k2 | 1386l3 | \([1, -1, 1, -1139, -14259]\) | \(223980311017/4278582\) | \(3119086278\) | \([2]\) | \(1024\) | \(0.61497\) | |
| 1386.k3 | 1386l2 | \([1, -1, 1, -149, 393]\) | \(498677257/213444\) | \(155600676\) | \([2, 2]\) | \(512\) | \(0.26839\) | |
| 1386.k4 | 1386l1 | \([1, -1, 1, 31, 33]\) | \(4657463/3696\) | \(-2694384\) | \([2]\) | \(256\) | \(-0.078180\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1386.k have rank \(0\).
Complex multiplication
The elliptic curves in class 1386.k do not have complex multiplication.Modular form 1386.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
