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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 6930.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6930.b1 | 6930f3 | \([1, -1, 0, -443520, 113799816]\) | \(13235378341603461121/9240\) | \(6735960\) | \([2]\) | \(24576\) | \(1.5233\) | |
6930.b2 | 6930f2 | \([1, -1, 0, -27720, 1783296]\) | \(3231355012744321/85377600\) | \(62240270400\) | \([2, 2]\) | \(12288\) | \(1.1767\) | |
6930.b3 | 6930f4 | \([1, -1, 0, -26640, 1927800]\) | \(-2868190647517441/527295615000\) | \(-384398503335000\) | \([2]\) | \(24576\) | \(1.5233\) | |
6930.b4 | 6930f1 | \([1, -1, 0, -1800, 25920]\) | \(885012508801/127733760\) | \(93117911040\) | \([2]\) | \(6144\) | \(0.83012\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6930.b have rank \(1\).
Complex multiplication
The elliptic curves in class 6930.b do not have complex multiplication.Modular form 6930.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.