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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 9576.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9576.c1 | 9576w3 | \([0, 0, 0, -11091, -449314]\) | \(202119559492/136857\) | \(102163203072\) | \([2]\) | \(16384\) | \(1.0505\) | |
9576.c2 | 9576w2 | \([0, 0, 0, -831, -4030]\) | \(340062928/159201\) | \(29710727424\) | \([2, 2]\) | \(8192\) | \(0.70393\) | |
9576.c3 | 9576w1 | \([0, 0, 0, -426, 3341]\) | \(733001728/10773\) | \(125656272\) | \([2]\) | \(4096\) | \(0.35735\) | \(\Gamma_0(N)\)-optimal |
9576.c4 | 9576w4 | \([0, 0, 0, 2949, -30490]\) | \(3799448348/2736741\) | \(-2042966209536\) | \([4]\) | \(16384\) | \(1.0505\) |
Rank
sage: E.rank()
The elliptic curves in class 9576.c have rank \(2\).
Complex multiplication
The elliptic curves in class 9576.c do not have complex multiplication.Modular form 9576.2.a.c
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.