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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 61200.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
61200.o1 | 61200cw1 | \([0, 0, 0, -1832250, 954509375]\) | \(29860725364736/3581577\) | \(81592801031250000\) | \([2]\) | \(1198080\) | \(2.2698\) | \(\Gamma_0(N)\)-optimal |
61200.o2 | 61200cw2 | \([0, 0, 0, -1680375, 1119293750]\) | \(-1439609866256/651714363\) | \(-237549885313500000000\) | \([2]\) | \(2396160\) | \(2.6164\) |
Rank
sage: E.rank()
The elliptic curves in class 61200.o have rank \(0\).
Complex multiplication
The elliptic curves in class 61200.o do not have complex multiplication.Modular form 61200.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.