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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 9386.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9386.j1 | 9386g3 | \([1, 1, 1, -165887, 25936485]\) | \(-10730978619193/6656\) | \(-313137383936\) | \([]\) | \(42768\) | \(1.5266\) | |
9386.j2 | 9386g2 | \([1, 1, 1, -1632, 49897]\) | \(-10218313/17576\) | \(-826878404456\) | \([]\) | \(14256\) | \(0.97730\) | |
9386.j3 | 9386g1 | \([1, 1, 1, 173, -1365]\) | \(12167/26\) | \(-1223192906\) | \([]\) | \(4752\) | \(0.42799\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9386.j have rank \(1\).
Complex multiplication
The elliptic curves in class 9386.j do not have complex multiplication.Modular form 9386.2.a.j
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.