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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 1850.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1850.o1 | 1850h1 | \([1, 1, 1, -1338, 18281]\) | \(-16954786009/370\) | \(-5781250\) | \([]\) | \(864\) | \(0.41351\) | \(\Gamma_0(N)\)-optimal |
1850.o2 | 1850h2 | \([1, 1, 1, -463, 42781]\) | \(-702595369/50653000\) | \(-791453125000\) | \([]\) | \(2592\) | \(0.96281\) | |
1850.o3 | 1850h3 | \([1, 1, 1, 4162, -1150469]\) | \(510273943271/37000000000\) | \(-578125000000000\) | \([]\) | \(7776\) | \(1.5121\) |
Rank
sage: E.rank()
The elliptic curves in class 1850.o have rank \(0\).
Complex multiplication
The elliptic curves in class 1850.o do not have complex multiplication.Modular form 1850.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.