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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 161700.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
161700.b1 | 161700er2 | \([0, -1, 0, -485622258, -4119264649863]\) | \(-8788102954619113216/954968814855\) | \(-1376301294711229713750000\) | \([]\) | \(47029248\) | \(3.6617\) | |
161700.b2 | 161700er1 | \([0, -1, 0, 580242, -17174157363]\) | \(14990845184/88418496375\) | \(-127428759080274093750000\) | \([]\) | \(15676416\) | \(3.1124\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 161700.b have rank \(0\).
Complex multiplication
The elliptic curves in class 161700.b do not have complex multiplication.Modular form 161700.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.