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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 28314cb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28314.bx2 | 28314cb1 | \([1, -1, 1, -2927, 93943]\) | \(-2146689/1664\) | \(-2149002700416\) | \([]\) | \(39200\) | \(1.0651\) | \(\Gamma_0(N)\)-optimal |
28314.bx1 | 28314cb2 | \([1, -1, 1, -231617, -47016197]\) | \(-1064019559329/125497034\) | \(-162075399615503946\) | \([]\) | \(274400\) | \(2.0380\) |
Rank
sage: E.rank()
The elliptic curves in class 28314cb have rank \(1\).
Complex multiplication
The elliptic curves in class 28314cb do not have complex multiplication.Modular form 28314.2.a.cb
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 Cremona 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 Cremona labels.