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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 15210.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15210.z1 | 15210z4 | \([1, -1, 1, -194213, -32893883]\) | \(8527173507/200\) | \(19001216309400\) | \([2]\) | \(103680\) | \(1.6600\) | |
15210.z2 | 15210z3 | \([1, -1, 1, -11693, -551339]\) | \(-1860867/320\) | \(-30401946095040\) | \([2]\) | \(51840\) | \(1.3134\) | |
15210.z3 | 15210z2 | \([1, -1, 1, -4088, 27317]\) | \(57960603/31250\) | \(4072620093750\) | \([2]\) | \(34560\) | \(1.1107\) | |
15210.z4 | 15210z1 | \([1, -1, 1, 982, 2981]\) | \(804357/500\) | \(-65161921500\) | \([2]\) | \(17280\) | \(0.76411\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15210.z have rank \(0\).
Complex multiplication
The elliptic curves in class 15210.z do not have complex multiplication.Modular form 15210.2.a.z
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.