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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 17600.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17600.bb1 | 17600w3 | \([0, -1, 0, -48524833, 130122917537]\) | \(-24680042791780949/369098752\) | \(-188978561024000000000\) | \([]\) | \(1152000\) | \(3.0276\) | |
17600.bb2 | 17600w1 | \([0, -1, 0, -44833, -3642463]\) | \(-19465109/22\) | \(-11264000000000\) | \([]\) | \(46080\) | \(1.4181\) | \(\Gamma_0(N)\)-optimal |
17600.bb3 | 17600w2 | \([0, -1, 0, 315167, 38237537]\) | \(6761990971/5153632\) | \(-2638659584000000000\) | \([]\) | \(230400\) | \(2.2228\) |
Rank
sage: E.rank()
The elliptic curves in class 17600.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 17600.bb do not have complex multiplication.Modular form 17600.2.a.bb
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.
\(\left(\begin{array}{rrr} 1 & 25 & 5 \\ 25 & 1 & 5 \\ 5 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.