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SageMath
E = EllipticCurve("el1")
E.isogeny_class()
Elliptic curves in class 161700.el
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
161700.el1 | 161700bc2 | \([0, 1, 0, -15108, 334788]\) | \(810448/363\) | \(170826348000000\) | \([2]\) | \(552960\) | \(1.4264\) | |
161700.el2 | 161700bc1 | \([0, 1, 0, 3267, 40788]\) | \(131072/99\) | \(-2911812750000\) | \([2]\) | \(276480\) | \(1.0798\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 161700.el have rank \(1\).
Complex multiplication
The elliptic curves in class 161700.el do not have complex multiplication.Modular form 161700.2.a.el
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.