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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 3850.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3850.a1 | 3850b1 | \([1, 1, 0, -515720, 142338880]\) | \(-606773969327363726065/14480963796992\) | \(-362024094924800\) | \([]\) | \(38880\) | \(1.9046\) | \(\Gamma_0(N)\)-optimal |
3850.a2 | 3850b2 | \([1, 1, 0, -168520, 330093440]\) | \(-21171034581520602865/1871407179898211648\) | \(-46785179497455291200\) | \([]\) | \(116640\) | \(2.4539\) |
Rank
sage: E.rank()
The elliptic curves in class 3850.a have rank \(1\).
Complex multiplication
The elliptic curves in class 3850.a do not have complex multiplication.Modular form 3850.2.a.a
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.