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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 4560.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4560.b1 | 4560n4 | \([0, -1, 0, -7411696, -4956797504]\) | \(10993009831928446009969/3767761230468750000\) | \(15432750000000000000000\) | \([2]\) | \(414720\) | \(2.9595\) | |
4560.b2 | 4560n2 | \([0, -1, 0, -6639856, -6583246400]\) | \(7903870428425797297009/886464000000\) | \(3630956544000000\) | \([2]\) | \(138240\) | \(2.4102\) | |
4560.b3 | 4560n1 | \([0, -1, 0, -413936, -103308864]\) | \(-1914980734749238129/20440940544000\) | \(-83726092468224000\) | \([2]\) | \(69120\) | \(2.0636\) | \(\Gamma_0(N)\)-optimal |
4560.b4 | 4560n3 | \([0, -1, 0, 1367824, -538943040]\) | \(69096190760262356111/70568821500000000\) | \(-289049892864000000000\) | \([2]\) | \(207360\) | \(2.6129\) |
Rank
sage: E.rank()
The elliptic curves in class 4560.b have rank \(0\).
Complex multiplication
The elliptic curves in class 4560.b do not have complex multiplication.Modular form 4560.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.