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SageMath
E = EllipticCurve("qg1")
E.isogeny_class()
Elliptic curves in class 366912.qg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
366912.qg1 | 366912qg1 | \([0, 0, 0, -153468, 22967280]\) | \(10536048/91\) | \(3452557054722048\) | \([2]\) | \(4128768\) | \(1.8059\) | \(\Gamma_0(N)\)-optimal |
366912.qg2 | 366912qg2 | \([0, 0, 0, -47628, 54084240]\) | \(-78732/8281\) | \(-1256730767918825472\) | \([2]\) | \(8257536\) | \(2.1524\) |
Rank
sage: E.rank()
The elliptic curves in class 366912.qg have rank \(0\).
Complex multiplication
The elliptic curves in class 366912.qg do not have complex multiplication.Modular form 366912.2.a.qg
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.