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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 13650.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13650.b1 | 13650e3 | \([1, 1, 0, -10425, 405375]\) | \(8020417344913/187278\) | \(2926218750\) | \([2]\) | \(24576\) | \(0.92869\) | |
13650.b2 | 13650e2 | \([1, 1, 0, -675, 5625]\) | \(2181825073/298116\) | \(4658062500\) | \([2, 2]\) | \(12288\) | \(0.58212\) | |
13650.b3 | 13650e1 | \([1, 1, 0, -175, -875]\) | \(38272753/4368\) | \(68250000\) | \([2]\) | \(6144\) | \(0.23554\) | \(\Gamma_0(N)\)-optimal |
13650.b4 | 13650e4 | \([1, 1, 0, 1075, 31875]\) | \(8780064047/32388174\) | \(-506065218750\) | \([2]\) | \(24576\) | \(0.92869\) |
Rank
sage: E.rank()
The elliptic curves in class 13650.b have rank \(2\).
Complex multiplication
The elliptic curves in class 13650.b do not have complex multiplication.Modular form 13650.2.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.