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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 47937.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47937.b1 | 47937b4 | \([1, 1, 1, -85379, 9566606]\) | \(115714886617/1539\) | \(915433091019\) | \([2]\) | \(150528\) | \(1.4386\) | |
47937.b2 | 47937b2 | \([1, 1, 1, -5484, 138996]\) | \(30664297/3249\) | \(1932580969929\) | \([2, 2]\) | \(75264\) | \(1.0921\) | |
47937.b3 | 47937b1 | \([1, 1, 1, -1279, -15748]\) | \(389017/57\) | \(33904929297\) | \([2]\) | \(37632\) | \(0.74549\) | \(\Gamma_0(N)\)-optimal |
47937.b4 | 47937b3 | \([1, 1, 1, 7131, 699102]\) | \(67419143/390963\) | \(-232553910048123\) | \([2]\) | \(150528\) | \(1.4386\) |
Rank
sage: E.rank()
The elliptic curves in class 47937.b have rank \(0\).
Complex multiplication
The elliptic curves in class 47937.b do not have complex multiplication.Modular form 47937.2.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.