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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 2240.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2240.o1 | 2240e3 | \([0, 0, 0, -332, 2256]\) | \(123505992/4375\) | \(143360000\) | \([4]\) | \(768\) | \(0.33574\) | |
2240.o2 | 2240e2 | \([0, 0, 0, -52, -96]\) | \(3796416/1225\) | \(5017600\) | \([2, 2]\) | \(384\) | \(-0.010833\) | |
2240.o3 | 2240e1 | \([0, 0, 0, -47, -124]\) | \(179406144/35\) | \(2240\) | \([2]\) | \(192\) | \(-0.35741\) | \(\Gamma_0(N)\)-optimal |
2240.o4 | 2240e4 | \([0, 0, 0, 148, -656]\) | \(10941048/12005\) | \(-393379840\) | \([2]\) | \(768\) | \(0.33574\) |
Rank
sage: E.rank()
The elliptic curves in class 2240.o have rank \(0\).
Complex multiplication
The elliptic curves in class 2240.o do not have complex multiplication.Modular form 2240.2.a.o
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.