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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 9576.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9576.w1 | 9576s1 | \([0, 0, 0, -22734, -1319355]\) | \(4126102419456/2527\) | \(795823056\) | \([2]\) | \(9216\) | \(1.0294\) | \(\Gamma_0(N)\)-optimal |
9576.w2 | 9576s2 | \([0, 0, 0, -22599, -1335798]\) | \(-253314541296/6385729\) | \(-32176717800192\) | \([2]\) | \(18432\) | \(1.3760\) |
Rank
sage: E.rank()
The elliptic curves in class 9576.w have rank \(0\).
Complex multiplication
The elliptic curves in class 9576.w do not have complex multiplication.Modular form 9576.2.a.w
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.