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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 273702.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
273702.ba1 | 273702ba2 | \([1, 0, 1, -19728581854, 1066575034826750]\) | \(-479352730263827621784814619569/214316023050990383094\) | \(-379673908112235574064389734\) | \([]\) | \(405672960\) | \(4.4405\) | |
273702.ba2 | 273702ba1 | \([1, 0, 1, 49825256, -10931905690]\) | \(7721758769769063671471/4497774542859970944\) | \(-7968081966923552985523584\) | \([]\) | \(57953280\) | \(3.4676\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 273702.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 273702.ba do not have complex multiplication.Modular form 273702.2.a.ba
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.