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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 960.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
960.n1 | 960p4 | \([0, 1, 0, -865, 9503]\) | \(546718898/405\) | \(53084160\) | \([4]\) | \(512\) | \(0.41598\) | |
960.n2 | 960p3 | \([0, 1, 0, -545, -5025]\) | \(136835858/1875\) | \(245760000\) | \([2]\) | \(512\) | \(0.41598\) | |
960.n3 | 960p2 | \([0, 1, 0, -65, 63]\) | \(470596/225\) | \(14745600\) | \([2, 2]\) | \(256\) | \(0.069403\) | |
960.n4 | 960p1 | \([0, 1, 0, 15, 15]\) | \(21296/15\) | \(-245760\) | \([2]\) | \(128\) | \(-0.27717\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 960.n have rank \(0\).
Complex multiplication
The elliptic curves in class 960.n do not have complex multiplication.Modular form 960.2.a.n
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.