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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 102960.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
102960.b1 | 102960da2 | \([0, 0, 0, -319323, 69453322]\) | \(1205943158724121/1258400\) | \(3757562265600\) | \([2]\) | \(552960\) | \(1.7028\) | |
102960.b2 | 102960da1 | \([0, 0, 0, -19803, 1102858]\) | \(-287626699801/9518080\) | \(-28420834590720\) | \([2]\) | \(276480\) | \(1.3562\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 102960.b have rank \(1\).
Complex multiplication
The elliptic curves in class 102960.b do not have complex multiplication.Modular form 102960.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.