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SageMath
E = EllipticCurve("jb1")
E.isogeny_class()
Elliptic curves in class 127050.jb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
127050.jb1 | 127050jg1 | \([1, 0, 0, -20633, -1136343]\) | \(4386781853/27216\) | \(6026850522000\) | \([2]\) | \(448000\) | \(1.2903\) | \(\Gamma_0(N)\)-optimal |
127050.jb2 | 127050jg2 | \([1, 0, 0, -8533, -2455243]\) | \(-310288733/11573604\) | \(-2562918184480500\) | \([2]\) | \(896000\) | \(1.6369\) |
Rank
sage: E.rank()
The elliptic curves in class 127050.jb have rank \(0\).
Complex multiplication
The elliptic curves in class 127050.jb do not have complex multiplication.Modular form 127050.2.a.jb
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.