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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 1050.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1050.b1 | 1050d1 | \([1, 1, 0, -4375, -113225]\) | \(-14822892630025/42\) | \(-26250\) | \([]\) | \(600\) | \(0.50455\) | \(\Gamma_0(N)\)-optimal |
1050.b2 | 1050d2 | \([1, 1, 0, 550, -343500]\) | \(46969655/130691232\) | \(-51051262500000\) | \([]\) | \(3000\) | \(1.3093\) |
Rank
sage: E.rank()
The elliptic curves in class 1050.b have rank \(0\).
Complex multiplication
The elliptic curves in class 1050.b do not have complex multiplication.Modular form 1050.2.a.b
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.