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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 26010.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26010.b1 | 26010c4 | \([1, -1, 0, -332115, -73583875]\) | \(8527173507/200\) | \(95019954125400\) | \([2]\) | \(221184\) | \(1.7941\) | |
26010.b2 | 26010c3 | \([1, -1, 0, -19995, -1234459]\) | \(-1860867/320\) | \(-152031926600640\) | \([2]\) | \(110592\) | \(1.4476\) | |
26010.b3 | 26010c2 | \([1, -1, 0, -6990, 60550]\) | \(57960603/31250\) | \(20366073843750\) | \([2]\) | \(73728\) | \(1.2448\) | |
26010.b4 | 26010c1 | \([1, -1, 0, 1680, 6796]\) | \(804357/500\) | \(-325857181500\) | \([2]\) | \(36864\) | \(0.89824\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 26010.b have rank \(1\).
Complex multiplication
The elliptic curves in class 26010.b do not have complex multiplication.Modular form 26010.2.a.b
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.