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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 126960.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
126960.b1 | 126960bn2 | \([0, -1, 0, -25011296, 8785125120]\) | \(234542659463/131220000\) | \(968078345163468226560000\) | \([2]\) | \(16957440\) | \(3.2927\) | |
126960.b2 | 126960bn1 | \([0, -1, 0, 6136224, 1085458176]\) | \(3463512697/2073600\) | \(-15298028170484436172800\) | \([2]\) | \(8478720\) | \(2.9461\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 126960.b have rank \(1\).
Complex multiplication
The elliptic curves in class 126960.b do not have complex multiplication.Modular form 126960.2.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.